Ch.9 Hypothesis Testing Populations Test Bank Answers nan - Business Stats Contemporary Decision 10e | Test Bank by Ken Black by Ken Black. DOCX document preview.
File: Ch09, Chapter 9: Statistical Inference: Hypothesis Testing for Single Populations
True/False
1. Hypotheses are tentative explanations of a principle operating in nature.
Response: See section 9.1 Introduction to Hypothesis Testing
Difficulty: Easy
Learning Objective: 9.1: Develop both one- and two-tailed statistical hypotheses that can be tested in a business setting by examining the rejection and non-rejection regions in light of Type I and Type II errors
2. The first step in testing a hypothesis is to establish a true null hypothesis and a false alternative hypothesis.
Response: See section 9.1 Introduction to Hypothesis Testing
Difficulty: Easy
Learning Objective: 9.1: Develop both one- and two-tailed statistical hypotheses that can be tested in a business setting by examining the rejection and non-rejection regions in light of Type I and Type II errors
3. In testing hypotheses, the researcher initially assumes that the alternative hypothesis is true and uses the sample data to reject it.
Response: See section 9.1 Introduction to Hypothesis Testing
Difficulty: Easy
Learning Objective: 9.1: Develop both one- and two-tailed statistical hypotheses that can be tested in a business setting by examining the rejection and non-rejection regions in light of Type I and Type II errors
4. The null and the alternative hypotheses must be mutually exclusive and collectively exhaustive.
Response: See section 9.1 Introduction to Hypothesis Testing
Difficulty: Medium
Learning Objective: 9.1: Develop both one- and two-tailed statistical hypotheses that can be tested in a business setting by examining the rejection and non-rejection regions in light of Type I and Type II errors
5. Generally speaking, the hypotheses that business researchers want to prove are stated in the alternative hypothesis.
Response: See section 9.1 Introduction to Hypothesis Testing
Difficulty: Medium
Learning Objective: 9.1: Develop both one- and two-tailed statistical hypotheses that can be tested in a business setting by examining the rejection and non-rejection regions in light of Type I and Type II errors
6. The probability of committing a Type I error is called the power of the test.
Response: See section 9.1 Introduction to Hypothesis Testing
Difficulty: Medium
Learning Objective: 9.1: Develop both one- and two-tailed statistical hypotheses that can be tested in a business setting by examining the rejection and non-rejection regions in light of Type I and Type II errors
7. When a true null hypothesis is rejected, the researcher has made a Type I error.
Response: See section 9.1 Introduction to Hypothesis Testing
Difficulty: Easy
Learning Objective: 9.1: Develop both one- and two-tailed statistical hypotheses that can be tested in a business setting by examining the rejection and non-rejection regions in light of Type I and Type II errors
8. When a false null hypothesis is rejected, the researcher has made a Type II error.
Response: See section 9.1 Introduction to Hypothesis Testing
Difficulty: Medium
Learning Objective: 9.1: Develop both one- and two-tailed statistical hypotheses that can be tested in a business setting by examining the rejection and non-rejection regions in light of Type I and Type II errors
9. When a researcher fails to reject a false null hypothesis, a Type II error has been committed.
Response: See section 9.1 Introduction to Hypothesis Testing
Difficulty: Easy
Learning Objective: 9.1: Develop both one- and two-tailed statistical hypotheses that can be tested in a business setting by examining the rejection and non-rejection regions in light of Type I and Type II errors
10. Power is equal to (1 –β), the probability of a test rejecting the null hypothesis that is indeed false.
Response: See section 9.1 Introduction to Hypothesis Testing
Difficulty: Medium
Learning Objective: 9.1: Develop both one- and two-tailed statistical hypotheses that can be tested in a business setting by examining the rejection and non-rejection regions in light of Type I and Type II errors
11. The rejection region for a hypothesis test becomes smaller if the level of significance is changed from 0.01 to 0.05.
Response: See section 9.1 Introduction to Hypothesis Testing
Difficulty: Hard
Learning Objective: 9.1: Develop both one- and two-tailed statistical hypotheses that can be tested in a business setting by examining the rejection and non-rejection regions in light of Type I and Type II errors
12. Whenever hypotheses are established such that the alternative hypothesis is "μ>8", where μ is the population mean, the hypothesis test would be a two-tailed test.
Response: See section 9.1 Introduction to Hypothesis Testing
Difficulty: Easy
Learning Objective:
9.1: Develop both one- and two-tailed statistical hypotheses that can be tested in a business setting by examining the rejection and non-rejection regions in light of Type I and Type II errors
13. Whenever hypotheses are established such that the alternative hypothesis is "μ ≠ 8", where μ is the population mean, the hypothesis test would be a two-tailed test.
Response:
See section 9.1 Introduction to Hypothesis Testing
Difficulty: Easy
Learning Objective:
9.1: Develop both one- and two-tailed statistical hypotheses that can be tested in a business setting by examining the rejection and non-rejection regions in light of Type I and Type II errors
14. The rejection and nonrejection regions are divided by a point called the critical value.
Response: See section 9.1 Introduction to Hypothesis Testing
Difficulty: Medium
Learning Objective:
9.1: Develop both one- and two-tailed statistical hypotheses that can be tested in a business setting by examining the rejection and non-rejection regions in light of Type I and Type II errors
15. The probability of type II error becomes bigger if the level of significance is changed from 0.01 to 0.05.
Response: See section 9.1 Introduction to Hypothesis Testing
Difficulty: Hard
Learning Objective: 9.1: Develop both one- and two-tailed statistical hypotheses that can be tested in a business setting by examining the rejection and non-rejection regions in light of Type I and Type II errors
16. Whenever hypotheses are established such that the alternative hypothesis is "μ > 8", where μ is the population mean, the p-value is the probability of observing a sample mean greater than the observed sample mean assuming that μ = 8.
Response: See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic ( Known)
Difficulty: Hard
Learning Objective: 9.2: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.
17. If a null hypothesis was not rejected at the 0.10 level of significance, it will be rejected at a 0.05 level of significance based on the same sample results.
Response: See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic ( Known)
Difficulty: Medium
Learning Objective: 9.2: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic
18. If a null hypothesis was rejected at the 0.025 level of significance, it will be rejected at a 0.01 level of significance based on the same sample results.
Response: See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic ( Known)
Difficulty: Medium
Learning Objective: 9.2: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic
19. If a null hypothesis is not rejected at the 0.05 level of significance, the p-value is bigger than 0.05
Response: See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic ( Known)
Difficulty: Hard
Learning Objective: 9.2: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic
20. In many cases a business researcher gathers data to test a hypothesis about a single population mean and the value of the population standard deviation is unknown. In this case the researcher cannot use the z test.
Response: See section 9.3 Testing Hypotheses about a Population Mean using the t Statistic ( unknown)
Difficulty: Easy
Learning Objective: 9.3: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic
21. When the population standard deviation ( ) is unknown, the value of s – 1 is used to compute the t value.
Response: See section 9.3 Testing Hypotheses about a Population Mean using the t Statistic ( unknown)
Difficulty: Easy
Learning Objective: 9.3: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic
22. In testing a hypothesis about a population mean with an unknown population standard deviation ( ) the degrees of freedom is used in the denominator of the test statistic.
Response: See section 9.3 Testing Hypotheses about a Population Mean using the t Statistic ( unknown)
Difficulty: Medium
Learning Objective: 9.3: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic
23. When using the t test to test a hypothesis about a population mean with an unknown population standard deviation ( ) the degrees of freedom is defined as n – 1.
Response: See section 9.3 Testing Hypotheses about a Population Mean using the t Statistic ( unknown)
Difficulty: Easy
Learning Objective: 9.3: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic
24. A z test of proportions is used when a hypothesis test is conducted on a population proportion.
Response: See section 9.4 Testing Hypotheses about a Proportion
Difficulty: Easy
Learning Objective: 9.4: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.
25. When conducting a hypothesis test on a population proportion, the value of q is defined as p + 1.
Response: See section 9.4 Testing Hypotheses about a Proportion
Difficulty: Easy
Learning Objective: 9.4: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.
26. In conducting the z test of proportions, the sample proportion is computed by dividing the number of items being counted by the estimated total population.
Response: See section 9.4 Testing Hypotheses about a Proportion
Difficulty: Medium
Learning Objective: 9.4: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.
27. Business researchers sometimes need to test for equality of population variance. The hypothesis test about a population variance is performed using a chi-square test.
Response: See section 9.5 Testing Hypotheses about a Variance
Difficulty: Easy
Learning Objective: 9.5: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.
28. In testing a hypothesis about a population variance, the chi-square test is fairly robust to the assumption the population is normally distributed.
Response: See section 9.5 Testing Hypotheses about a Variance
Difficulty: Medium
Learning Objective: 9.5: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.
29. If car manufacturer of cars orders the windshields from another company. The width of the windshields received need to be within 0.2 mm of the average width. The contract between the car manufacturer and the windshield suppler should include a clause related to the delivered windshields’ median.
Ans: False
Response: See section 9.5 Testing Hypotheses about a Variance
Difficulty: Medium
Learning Objective: 9.5: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.
30. If the observed chi-squared value is more than the critical chi-squared value found on the related table, then the null hypothesis is rejected.
Ans: True
Response: See section 9.5 Testing Hypotheses about a Variance
Difficulty: Medium
Learning Objective: 9.5: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.
31. The value of committing a Type II error is defined by the researcher prior to the study.
Response: See section 9.6 Solving for Type II Errors.
Difficulty: Easy
Learning Objective: 9.6: Solve for possible Type II errors when failing to reject the null hypothesis.
3. The probability of committing a Type II error changes for each alternative value of the parameter.
Response: See section 9.6 Solving for Type II Errors.
Difficulty: Medium
Learning Objective: 9.6: Solve for possible Type II errors when failing to reject the null hypothesis.
3. Increasing the sample size reduces the probability of committing a Type I and Type II simultaneously.
Response: See section 9.6 Solving for Type II Errors.
Difficulty: Easy
Learning Objective: 9.6: Solve for possible Type II errors when failing to reject the null hypothesis.
34. If the null hypothesis is in reality false, but the sample data leads the analyst to fail to reject the null, then the analysts has made a Type II error.
Ans: True
Response: See section 9.6 Solving for Type II Errors.
Difficulty: Easy
Learning Objective: 9.6: Solve for possible Type II errors when failing to reject the null hypothesis.
35. A business is testing a new product that in reality would make the company money. Based on market research data, the business analyst committed a Type II error by rejecting the null.
Ans: False
Response: See section 9.6 Solving for Type II Errors.
Difficulty: Easy
Learning Objective: 9.6: Solve for possible Type II errors when failing to reject the null hypothesis.
Multiple Choice
36. A “scientific hypothesis” _______________.
a) is a synonym for the term “scientific theory.”
b) is disproven if a counterexample is found.
c) is a tentative explanation of some natural phenomena.
d) is a proven explanation of some natural phenomena.
e) may or may not be testable.
Response: See section 9.1 Introduction to Hypothesis Testing
Difficulty: Medium
Bloom’s level: Knowledge
Learning Objective: 9.1: Develop both one- and two-tailed statistical hypotheses that can be tested in a business setting by examining the rejection and nonrejection regions in light of Type I and Type II errors.
37. A statistically significant result is _______________.
a) a result that is likely due to chance.
b) a result that is unlikely due to chance.
c) the same as a substantive result.
d) a result that is important for decision makers.
e) a result that leads to the rejection of the alternative hypothesis.
Response: See section 9.1 Introduction to Hypothesis Testing
Difficulty: Easy
Bloom’s level: Knowledge
Learning Objective: 9.1: Develop both one- and two-tailed statistical hypotheses that can be tested in a business setting by examining the rejection and nonrejection regions in light of Type I and Type II errors.
38. Suppose that
Ho: ≤ 0.01
Ha: > 0.01
The value 0.01 is the maximum safe level of some naturally occurring lethal pollutant in drinking water for human consumption. You need to decide if you will use water coming from a specific source for one of the beverages your company produces, based on sample measures of this pollutant taken in random different locations and times at the source of water. In this case you would want to
a) maximize the power of the test.
b) maximize β.
c) minimize .
d) maximize the significance, α.
e) maximize 1 – α.
Response: See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic ( Known)
Difficulty: Medium
Bloom’s level: Application
Learning Objective: 9.2: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.
39. If the p-value for a one-tailed test is 0.019, then the null hypothesis
a) can be rejected at a significance level of 0.01.
b) would be rejected or not rejected depending on the value of the statistic (the observed value).
c) would be rejected or not rejected depending on the value of the statistic and the critical value.
d) can be rejected at a significance level of 0.10.
e) may or may not be rejected, but there is no enough information to answer this question.
Response: See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic ( Known)
Difficulty: Medium
Bloom’s level: Application
Learning Objective: 9.2: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.
40. The p-value is
a) the probability that the alternative hypothesis is true.
b) the probability that the null hypothesis is true.
c) the probability of a statistic being at most as extreme as the observed value when Ho is true.
d) the probability of a statistic being at most as extreme as the observed value when Ho is false.
e) the probability of a statistic being at least as extreme as the observed value when Ho is true.
Response: See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic ( Known)
Difficulty: Medium
Bloom’s level: Knowledge
Learning Objective: 9.2: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.
41. The customer help center in your company receives calls from customers who need help with some of the customized software solutions your company provides. Your company claims that the average waiting time is 7 minutes at the busiest time, from 8 a.m. to 10 a.m., Monday through Thursday. One of your main clients has recently complained that every time she calls during the busy hours, the waiting time exceeds 7 minutes. You conduct a statistical study to determine the average waiting time with a sample of 35 calls for which you obtain an average waiting time of 8.15 minutes. If the population standard deviation is known to be 4.2 minutes, and α = 0.05, the p-value is approximately
a) 0.025
b) 0.026
c) 0.05
d) 0.053
e) 0.10
Response: See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic ( Known)
Difficulty: Hard
Bloom’s level: Application
Learning Objective: 9.2: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.
42. The customer help center in your company receives calls from customers who need help with some of the customized software solutions your company provides. Your company claims that the average waiting time is 7 minutes at the busiest time, from 8 a.m. to 10 a.m., Monday through Thursday. One of your main clients has recently complained that every time she calls during the busy hours, the waiting time exceeds 7 minutes. You conduct a statistical study to determine the average waiting time with a sample of 35 calls for which you obtain an average waiting time of 8.15 minutes. If the population standard deviation is known to be 4.2 minutes, and α = 0.05, the appropriate decision is to ___________.
a) increase the sample size
b) reduce the sample size
c) fail to reject the 7-minute average waiting time claim
d) maintain status quo
e) reject the 7-minute claim
Response: See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic ( Known)
Difficulty: Hard
Bloom’s level: Application
Learning Objective: 9.2: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.
43. Consider the following null and alternative hypotheses.
Ho: ≤ 67
Ha: > 67
These hypotheses _______________.
a) indicate a one-tailed test with a rejection area in the right tail
b) indicate a one-tailed test with a rejection area in the left tail
c) indicate a two-tailed test
d) are established incorrectly
e) are not mutually exclusive
Response: See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic ( Known)
Difficulty: Easy
Learning Objective: 9.2: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.
44. Consider the following null and alternative hypotheses.
Ho: ≥ 67
Ha: < 67
These hypotheses _______________.
a) indicate a one-tailed test with a rejection area in the right tail
b) indicate a one-tailed test with a rejection area in the left tail
c) indicate a two-tailed test
d) are established incorrectly
e) are not mutually exclusive
Response: See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic ( Known)
Difficulty: Easy
Learning Objective: 9.2: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.
45. Consider the following null and alternative hypotheses.
Ho: = 67
Ha: ≠ 67
These hypotheses ______________.
a) indicate a one-tailed test with a rejection area in the right tail
b) indicate a one-tailed test with a rejection area in the left tail
c) indicate a two-tailed test
d) are established incorrectly
e) are not mutually exclusive
Response: See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic ( Known)
Difficulty: Easy
Learning Objective: 9.2: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.
46. In a two-tailed hypothesis about a population mean with a sample size of 100, is known, and α = 0.10, the rejection region would be _______.
a) z > 1.64
b) z > 1.28
c) z < -1.28 and z > 1.28
d) z < -1.64 and z > 1.64
e) z < -2.33 and z > 2.33
Response: See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic ( Known)
Difficulty: Medium
Learning Objective: 9.2: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.
47. In a two-tailed hypothesis about a population mean with a sample size of 100, is known, and α = 0.05, the rejection region would be _______.
a) z > 1.64
b) z > 1.96
c) z < -1.96 and z > 1.96
d) z < -1.64 and z > 1.64
e) z < -2.33 and z > 2.33
Response: See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic ( Known)
Difficulty: Medium
Learning Objective: 9.2: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.
48. Suppose you are testing the null hypothesis that a population mean is less than or equal to 46, against the alternative hypothesis that the population mean is greater than 46. If the sample size is 25, is known, and α = .01, the critical value of z is _______.
a) 1.645
b) -1.645
c) 1.28
d) -2.33
e) 2.33
Response: See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic ( Known)
Difficulty: Medium
Learning Objective: 9.2: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.
49. Suppose you are testing the null hypothesis that a population mean is less than or equal to 46, against the alternative hypothesis that the population mean is greater than 46. The sample size is 25 and α =.05. If the sample mean is 50 and the population standard deviation is 8, the observed z value is _______.
a) 2.5
b) -2.5
c) 6.25
d) -6.25
e) 12.5
Response: See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic ( Known)
Difficulty: Medium
Learning Objective: 9.2: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.
50. Suppose you are testing the null hypothesis that a population mean is greater than or equal to 60, against the alternative hypothesis that the population mean is less than 60. The sample size is 64 and α = .05. If the sample mean is 58 and the population standard deviation is 16, the observed z value is _______.
a) -1
b) 1
c) -8
d) 8
e) 58
Response: See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic ( Known)
Difficulty: Medium
Learning Objective: 9.2: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.
51. A researcher is testing a hypothesis of a single mean. The critical z value for
α = .05 in a one‑tailed test is 1.645. The observed z value from sample data is 1.13. The decision made by the researcher based on this information is to ______ the null hypothesis.
a) reject
b) fail to reject
c) redefine
d) change the alternate hypothesis
e) restate
Response: See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic ( Known)
Difficulty: Medium
Learning Objective: 9.2: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.
52. A researcher is testing a hypothesis of a single mean. The critical z value for
α = .05 in a two‑tailed test is +1.96. The observed z value from sample data is ‑1.85. The decision made by the researcher based on this information is to _____ the null hypothesis.
a) reject
b) fail to reject
c) redefine
d) change the alternate hypothesis
e) restate
Response: See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic ( Known)
Difficulty: Medium
Learning Objective: 9.2: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.
53. A researcher is testing a hypothesis of a single mean. The critical z value for
α = .05 in a two‑tailed test is +1.96. The observed z value from sample data is 2.85. The decision made by the researcher based on this information is to _____ the null hypothesis.
a) reject
b) fail to reject
c) redefine
d) change the alternate hypothesis
e) restate
Response: See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic ( Known)
Difficulty: Medium
Learning Objective: 9.2: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.
54. A researcher is testing a hypothesis of a single mean. The critical z value for α = .05 in a two‑tailed test is +1.96. The observed z value from sample data is -2.11. The decision made by the researcher based on this information is to _____ the null hypothesis.
a) reject
b) fail to reject
c) redefine
d) change the alternate hypothesis
e) restate
Response: See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic ( Known)
Difficulty: Medium
Learning Objective: 9.2: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.
55. A coffee-dispensing machine is supposed to deliver 8 ounces of liquid into each paper cup, but a consumer believes that the actual mean amount is less. The consumer obtained a sample of 49 cups of the dispensed liquid with average of 7.75 ounces. If the sample variance of the dispensed liquid per cup is 0.81 ounces, and α = 0.05, the p-value is approximately __________.
- 0.05
- 0.025
- 0.06
- 0.015
- 0.10
Response: See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic ( Known)
Difficulty: Hard
Learning Objective: 9.2: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.
56. A coffee-dispensing machine is supposed to deliver 8 ounces of liquid into each paper cup, but a consumer believes that the actual mean amount is less. The consumer obtained a sample of 49 cups of the dispensed liquid with average of 7.75 ounces. If the sample variance of the dispensed liquid delivered per cup is 0.81 ounces, and α = 0.05, the appropriate decision is to ________.
a) increase the sample size
b) reduce the sample size
c) fail to reject the 8-ounces claim
d) maintain status quo
e) reject the 8-ounces claim
Response: See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic ( Known)
Difficulty: Hard
Learning Objective: 9.2: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.
57. The local swim team is considering offering a new semi-private class aimed at entry-level swimmers, but needs at minimum number of swimmers to sign up in order to be cost effective. Last year’s data showed that during 8 swim sessions the average number of entry-level swimmers attending was 15. Suppose the instructor wants to conduct a hypothesis test. The alternative hypothesis for this hypothesis test is: "the population mean is less than 15". The sample size is 8, is known, and α =.05, the critical value of z is _______.
a) 1.645
b) -1.645
c) 1.96
d) -1.96
e) 2.05
Response: See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic ( Known)
Difficulty: Medium
Learning Objective: 9.2: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.
58. The local swim team is considering offering a new semi-private class aimed at entry-level swimmers, but needs a minimum number of swimmers to sign up in order to be cost effective. Last year’s data showed that during 8 swim sessions the average number of entry-level swimmers attending was 15. Suppose the instructor wants to conduct a hypothesis test and the alternative hypothesis is "the population mean is greater than 15." If the sample size is 5, is known, and α = .01, the critical value of z is _______.
a) 2.575
b) -2.575
c) 2.33
d) -2.33
e) 2.45
Response: See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic ( Known)
Difficulty: Medium
Learning Objective: 9.2: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.
59. A home building company routinely orders standard interior doors with a height of 80 inches. Recently the installers have complained that the doors are not the standard height. The quality control inspector for the home building company is concerned that the manufacturer is supplying doors that are not 80 inches in height. In an effort to test this, the inspector is going to gather a sample of the recently received doors and measure the height. The alternative hypothesis for the statistical test to determine if the doors are not 80 inches is __________.
a) the mean height is > 80 inches
b) the mean height is < 80 inches
c) the mean height is = 80 inches
d) the mean height is ≠ 80 inches
e) the mean height is ≥ 80 inches
Response: See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic ( Known)
Difficulty: Medium
Learning Objective: 9.2: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.
60. Jennifer Cantu, VP of Customer Services at Tri-State Auto Insurance, Inc., monitors the claims processing time of the claims division. Her standard includes "a mean processing time of 5 days or less." Each week, her staff checks for compliance by analyzing a random sample of 60 claims. Jennifer's null hypothesis is ________.
a) μ > 5
b) σ > 5
c) n = 60
d) μ < 5
e) μ = =5
Response: See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic ( Known)
Difficulty: Medium
Learning Objective: 9.2: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.
61. The customer help center in your company receives calls from customers who need help with some of the customized software solutions your company provides. Your company claims that the average waiting time is 7 minutes at the busiest time, from 8 a.m. to 10 a.m., Monday through Thursday. One of your main clients has recently complained that every time she calls during the busy hours, the waiting time exceeds 7 minutes. You conduct a statistical study to determine the average waiting time with a sample of 35 calls, for which you obtain an average waiting time of 8.15 minutes. Suppose that you can assume that waiting times are normally distributed. The sample standard deviation is 4.2 minutes. The null hypothesis is:
a) n ≠ 35
b) n = 35
c) μ = 7
d) μ ≠ 7
e) > 7
Response: See section 9.3 Testing Hypotheses about a Population Mean using the t Statistic ( Unknown)
Difficulty: Easy
Bloom’s level: Knowledge
Learning Objective: 9.3: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.
62. In performing a hypothesis test where the null hypothesis is that the population mean is 23 against the alternative hypothesis that the population mean is not equal to 23, a random sample of 17 items is selected. The sample mean is 24.6 and the sample standard deviation is 3.3. It can be assumed that the population is normally distributed. The degrees of freedom associated with this are _______.
a) 17
b) 16
c) 15
d) 2
e) 1
Response: See section 9.3 Testing Hypotheses about a Population Mean using the t Statistic ( Unknown)
Difficulty: Easy
Learning Objective: 9.3: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.
63. In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is not equal to 4.8, a random sample of 25 items is selected. The sample mean is 4.1 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The degrees of freedom associated with this are _______.
a) 25
b) 24
c) 26
d) 2
e) 1
Response: See section 9.3 Testing Hypotheses about a Population Mean using the t Statistic ( Unknown)
Difficulty: Easy
Learning Objective: 9.3: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.
64 In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is not equal to 4.8, a random sample of 25 items is selected. The sample mean is 4.1 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The level of significance is selected to be 0.10. The critical value found in the “t” table "t" for this problem is _______.
a) 1.318
b) 1.711
c) 2.492
d) 2.797
e) 3.227
Response: See section 9.3 Testing Hypotheses about a Population Mean using the t Statistic ( Unknown)
Difficulty: Medium
Learning Objective: 9.3: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.
65. In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is not equal to 4.8, a random sample of 25 items is selected. The sample mean is 4.1 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The observed "t" value for this problem is _______.
a) -12.5
b) 12.5
c) -2.5
d) -0.7
e) 0.7
Response: See section 9.3 Testing Hypotheses about a Population Mean using the t Statistic ( Unknown)
Difficulty: Medium
Learning Objective: 9.3: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.
66. In performing hypothesis tests about the population mean, if the population standard deviation is not known, a t test can be used to test the mean if _________________.
a) n is small
b) the sample is random
c) the population mean is known
d) the population is normally distributed
e) the population is chi-square distributed
Response: See section 9.3 Testing Hypotheses about a Population Mean using the t Statistic ( Unknown)
Difficulty: Medium
Learning Objective: 9.3: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.
67. Suppose a researcher is testing a null hypothesis that = 61. A random sample of n = 36 is taken resulting in a sample mean of 63 and s = 9. The observed test statistic is _______.
a) -0.22
b) 0.22
c) 1.33
d) 8.08
e) 7.58
Response: See section 9.3 Testing Hypotheses about a Population Mean using the t Statistic ( Unknown)
Difficulty: Medium
Learning Objective: 9.3: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.
68. The local oil changing business is very busy on Saturday mornings and is considering expanding. A national study of similar businesses reported the mean number of customers waiting to have their oil changed on Saturday morning is 3.6. Suppose the local oil changing business owner, wants to perform a hypothesis test. The null hypothesis is the population mean is 3.6 and the alternative hypothesis that the population mean is not equal to 3.6. The owner takes a random sample of 16 Saturday mornings during the past year and determines the sample mean is 4.2 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The observed "t" value for this problem is _______.
a) 0.05
b) 0.43
c) 1.71
d) 1.33
e) 0.71
Response: See section 9.3 Testing Hypotheses about a Population Mean using the t Statistic ( Unknown)
Difficulty: Medium
Learning Objective: 9.3: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.
69. The local oil changing business is very busy on Saturday mornings and is considering expanding. A national study of similar businesses reported the mean number of customers waiting to have their oil changed on Saturday morning is 3.6. Suppose the local oil changing business owner, wants to perform a hypothesis test. The null hypothesis is the population mean is 3.6 and the alternative hypothesis that the population mean is not equal to 3.6. The owner takes a random sample of 16 Saturday mornings during the past year and determines the sample mean is 4.2 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed and the level of significance is 0.05. The critical value found in the "t" table for this problem is _______.
a) 1.753
b) 2.947
c) 2.120
d) 2.131
e) 2.311
Response: See section 9.3 Testing Hypotheses about a Population Mean using the t Statistic ( Unknown)
Difficulty: Medium
Learning Objective: 9.3: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.
70. The local oil changing business is very busy on Saturday mornings and is considering expanding. A national study of similar businesses reported the mean number of customers waiting to have their oil changed on Saturday morning is 3.6. Suppose the local oil changing business owner, wants to perform a hypothesis test. The null hypothesis is the population mean is 3.6 and the alternative hypothesis is the population mean is not equal to 3.6. The owner takes a random sample of 16 Saturday mornings during the past year and determines the sample mean is 4.2 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The level of significance is 0.05. The decision rule for this problem is to reject the null hypothesis if the observed "t" value is _______.
a) less than -2.131 or greater than 2.131
b) less than -1.761 or greater than 1.761
c) less than -1.753 or greater than 1.753
d) less than -2.120 or greater than 2.120
e) less than -3.120 or greater than 3.120
Response: See section 9.3 Testing Hypotheses about a Population Mean using the t Statistic ( Unknown)
Difficulty: Medium
Learning Objective: 9.3: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.
71. A coffee-dispensing machine is supposed to deliver 8 ounces of liquid into each paper cup, but a consumer believes that the actual mean amount is less. The consumer obtained a sample of 16 cups of the dispensed liquid with sample mean of 7.75 ounces and sample variance of 0.81 ounces. If the dispensed liquid delivered per cup is normally distributed, the appropriate decision at α = 0.05 is to ___________.
a) increase the sample size
b) reduce the sample size
c) fail to reject the 8-ounces claim
d) maintain status quo
e) reject the 8-ounces claim
Response: See section 9.3 Testing Hypotheses about a Population Mean using the t Statistic ( Unknown)
Difficulty: Hard
Learning Objective: 9.3: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.
72. The weight of a USB flash drive is 30 grams and is normally distributed. Periodically, quality control inspectors at Dallas Flash Drives randomly select a sample of 17 USB flash drives. If the mean weight of the USB flash drives is too heavy or too light the machinery is shut down for adjustment; otherwise, the production process continues. The last sample showed a mean and standard deviation of 31.9 and 1.8 grams, respectively. Using α = 0.10, the critical "t" values are _______.
a) -2.120 and 2.120
b) -2.131 and 2.131
c) -1.753 and 1.753
d) -1.746 and 1.746
e) -2.567 and 2.567
Response: See section 9.3 Testing Hypotheses about a Population Mean using the t Statistic ( Unknown)
Difficulty: Medium
Learning Objective: 9.3: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.
73. The weight of a USB flash drive is 30 grams and is normally distributed. Periodically, quality control inspectors at Dallas Flash Drives randomly select a sample of 17 USB flash drives. If the mean weight of the USB flash drives is too heavy or too light the machinery is shut down for adjustment; otherwise, the production process continues. The last sample showed a mean and standard deviation of 31.9 and 1.8 grams, respectively. The null hypothesis is ______.
a) n ≠ 17
b) n = 17
c) μ = 30
d) μ ≠ 30
e) ≥ 34.9
Response: See section 9.3 Testing Hypotheses about a Population Mean using the t Statistic ( Unknown)
Difficulty: Easy
Learning Objective: 9.3: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.
74. The weight of a USB flash drive is 30 grams and is normally distributed. Periodically, quality control inspectors at Dallas Flash Drives randomly select a sample of 17 USB flash drives. If the mean weight of the USB flash drives is too heavy or too light the machinery is shut down for adjustment; otherwise, the production process continues. The last sample showed a mean and standard deviation of 31.9 and 1.8 grams, respectively. Using α = 0.10, the appropriate decision is to _______.
a) reject the null hypothesis and shut down the process
b) reject the null hypothesis and do not shut down the process
c) fail to reject the null hypothesis and shut down the process
d) fail to reject the null hypothesis and do not shut down the process) do nothing
Response: See section 9.3 Testing Hypotheses about a Population Mean using the t Statistic ( Unknown)
Difficulty: Hard
Learning Objective: 9.3: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.
75. The customer help center in your company receives calls from customers who need help with some of the customized software solutions your company provides. Previous studies had indicated that 20% of customers who call the help center are Hispanics whose native language is Spanish and therefore would prefer to talk to a Spanish-speaking representative. This figure coincides with the national proportion, as shown by multiple larger polls. You want to test the hypothesis that 20% of the callers would prefer to talk to a Spanish-speaking representative. You conduct a statistical study with a sample of 35 calls and find out that 11 of the callers would prefer a Spanish-speaking representative. The significance level for this test is 0.01. The value of the test statistic obtained is:
a) 0.008
b) 0.29
c) 0.58
d) 1.69
e) 1.73
Response: See section 9.4 Testing Hypotheses about a Proportion
Difficulty: Medium
Bloom’s level: Application
Learning Objective: 9.4: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.
76. A political scientist wants to prove that a candidate is currently carrying more than 60% of the vote in the state. She has her assistants randomly sample 200 eligible voters in the state by telephone and only 90 declare that they support her candidate. The observed z value for this problem is _______.
a) -4.33
b) 4.33
c) 0.45
d) -.31
e) 2.33
Response: See section 9.4 Testing Hypotheses about a Proportion
Difficulty: Medium
Learning Objective: 9.4: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.
77. A company believes that it controls more than 30% of the total market share for one of its products. To prove this belief, a random sample of 144 purchases of this product is contacted. It is found that 50 of the 144 purchases were of this company's brand. If a researcher wants to conduct a statistical test for this problem, the alternative hypothesis would be _______.
a) the population proportion is less than 0.30
b) the population proportion is greater than 0.30
c) the population proportion is not equal to 0.30
d) the population mean is less than 40
e) the population mean is greater than 40
Response: See section 9.4 Testing Hypotheses about a Proportion
Difficulty: Easy
Learning Objective: 9.4: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.
78. A company believes that it controls more than 30% of the total market share for one of its products. To prove this belief, a random sample of 144 purchases of this product is contacted. It is found that 50 of the 144 purchases were of this company's brand. If a researcher wants to conduct a statistical test for this problem, the observed z value would be _______.
a) 0.05
b) 0.103
c) 0.35
d) 1.24
e) 1.67
Response: See section 9.4 Testing Hypotheses about a Proportion
Difficulty: Medium
Learning Objective: 9.4: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.
79. A company believes that it controls more than 30% of the total market share for one of its products. To prove this belief, a random sample of 144 purchases of this product is contacted. It is found that 50 of the 144 purchases were of this company's brand. If a researcher wants to conduct a statistical test for this problem, the test would be _______.
a) a one-tailed test
b) a two-tailed test
c) an alpha test
d) a finite population test
e) a finite sample test
Response: See section 9.4 Testing Hypotheses about a Proportion
Difficulty: Easy
Learning Objective: 9.4: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.
80. A small restaurant owner believes no more than 36% of his customers travel over 10 miles to his business. He is interested in expanding his customer base through marketing. However, he would like to test his hypothesis prior to investing money in a marketing initiative. He intends to use the following null and alternative hypotheses.
Ho: p ≤ 0.36
Ha: p > 0.36
These hypotheses _______________.
a) indicate a one-tailed test with a rejection area in the right tail
b) indicate a one-tailed test with a rejection area in the left tail
c) indicate a two-tailed test
d) are established incorrectly
e) are not mutually exclusive
Response: See section 9.4 Testing Hypotheses about a Population Proportion
Difficulty: Easy
Learning Objective: 9.4: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.
81. A small restaurant owner believes at least 36 % of his customers would be willing to order take out service if it were available. He is interested in surveying his customer base. He intends to use the following null and alternative hypotheses.
Ho: p ≥ 0.36
Ha: p < 0.36
These hypotheses _______________.
a) indicate a one-tailed test with a rejection area in the right tail
b) indicate a one-tailed test with a rejection area in the left tail
c) indicate a two-tailed test
d) are established incorrectly
e) are not mutually exclusive
Response: See section 9.4 Testing Hypotheses about a Population Proportion
Difficulty: Easy
Learning Objective: 9.4: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.
82. A small restaurant owner believes exactly 36 % of his customers come to the restaurant because of his daily half-price specials. He is interested in expanding his daily specials and increasing the price. However, he would like to test his hypothesis prior to expanding the daily special offerings. He intends to use the following null and alternative hypotheses.
Ho: p = 0.36
Ha: p ≠ 0.36
These hypotheses _______________.
a) indicate a one-tailed test with a rejection area in the right tail
b) indicate a one-tailed test with a rejection area in the left tail
c) indicate a two-tailed test
d) are established incorrectly
e) are not mutually exclusive
Response: See section 9.4 Testing Hypotheses about a Population Proportion
Difficulty: Easy
Learning Objective: 9.4: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.
83. Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standards is "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Ophelia's null hypothesis is _______.
a) p > 0.05
b) p = =0.05
c) n = 30
d) n = 500
e) n = 0.05
Response: See section 9.4 Testing Hypotheses about a Proportion
Difficulty: Easy
Learning Objective: 9.4: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.
84. Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standards is "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Using α = 0.10, the critical z value is _______.
a) 1.645
b) -1.645
c) 1.28
d) -1.28
e) 2.28
Response: See section 9.4 Testing Hypotheses about a Proportion
Difficulty: Medium
Learning Objective: 9.4: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.
85. Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standards is "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Using α = 0.10, the observed z value is _______.
a) 1.03
b) -1.03
c) 0.046
d) -0.046
e) 1.33
Response: See section 9.4 Testing Hypotheses about a Proportion
Difficulty: Medium
Learning Objective: 9.4: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.
86. Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standards is "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Using α = 0.10, the appropriate decision is to _______.
a) reduce the sample size
b) increase the sample size
c) reject the null hypothesis
d) fail to reject the null hypothesis
e) do nothing
Response: See section 9.4 Testing Hypotheses about a Proportion
Difficulty: Hard
Learning Objective: 9.4: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.
87. Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standards is "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 38 defaulted loans. Using α = 0.10, the appropriate decision is to _______.
a) reduce the sample size
b) increase the sample size
c) reject the null hypothesis
d) fail to reject the null hypothesis
e) do nothing
Response: See section 9.4 Testing Hypotheses about a Proportion
Difficulty: Hard
Learning Objective: 9.4: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.
88. The executives of CareFree Insurance, Inc. feel that "a majority of our employees perceive a participatory management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis at the 0.05 level of significance. Eighty employees rate the management as participatory. The null hypothesis is __________.
a) n = 30
b) n = 200
c) p = 0.50
d) p < 0.50
e) n > 200
Response: See section 9.4 Testing Hypotheses about a Proportion
Difficulty: Easy
Learning Objective: 9.4: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.
89. The executives of CareFree Insurance, Inc. feel that "a majority of our employees perceive a participatory management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis at the 0.05 level of significance. Eighty employees rate the management as participatory. The appropriate decision is to __________.
a) fail to reject the null hypothesis
b) reject the null hypothesis
c) reduce the sample size
d) increase the sample size
e) do nothing
Response: See section 9.4 Testing Hypotheses about a Proportion
Difficulty: Hard
Learning Objective: 9.4: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.
90. The executives of CareFree Insurance, Inc. feel that "a majority of our employees perceive a participatory management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis at the 0.05 level of significance. Ninety employees rate the management as participatory. The appropriate decision is to __________.
a) fail to reject the null hypothesis
b) reject the null hypothesis
c) reduce the sample size
d) increase the sample size
e) maintain status quo
Response: See section 9.4 Testing Hypotheses about a Proportion
Difficulty: Hard
Learning Objective: 9.4: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.
91. Elwin Osbourne, CIO at GFS, Inc., suspects that at least 25% of e-mail messages sent by GFS employees are not business related. A random sample of 300 e-mail messages was selected to test this hypothesis at the 0.01 level of significance. Fifty-four of the messages were not business related. The null hypothesis is ____.
a) = 30
b) n = 300
c) p < 0.25
d) p ≠ 0.25
e) p = 0.25
Response: See section 9.4 Testing Hypotheses about a Proportion
Difficulty: Easy
Learning Objective: 9.4: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.
92. Elwin Osbourne, CIO at GFS, Inc., suspects that at least 25% of e-mail messages sent by GFS employees are not business related. A random sample of 300 e-mail messages was selected to test this hypothesis at the 0.01 level of significance. Fifty-four of the messages were not business related. The appropriate decision is to _______.
a) increase the sample size
b) gather more data
c) reject the null hypothesis
d) fail to reject the null hypothesis
e) maintain status quo
Response: See section 9.4 Testing Hypotheses about a Proportion
Difficulty: Hard
Learning Objective: 9.4: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.
93. Elwin Osbourne, CIO at GFS, Inc., suspects that at least 25% of e-mail messages sent by GFS employees are not business related. A random sample of 300 e-mail messages was selected to test this hypothesis at the 0.01 level of significance. Sixty of the messages were not business related. The appropriate decision is to _______.
a) increase the sample size
b) gather more data
c) maintain status quo
d) fail to reject the null hypothesis
e) reject the null hypothesis
Response: See section 9.4 Testing Hypotheses about a Proportion
Difficulty: Hard
Learning Objective: 9.4: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.
94. Discrete Components, Inc. manufactures a line of electrical resistors. Presently, the carbon composition line is producing 100-ohm resistors. The population variance of these resistors "must not exceed 4" to conform to industry standards. Periodically, the quality control inspectors check for conformity by randomly selecting 10 resistors from the line, and calculating the sample variance. The last sample had a variance of 4.36. Assume that the population is normally distributed. Using α = 0.05, the null hypothesis is _________________.
a) μ = 100
b) σ ≤ 10
c) s2 ≥ 4
d) σ2 = = 4
e) n = 100
Response: See section 9.5 Testing Hypotheses about a Variance
Difficulty: Easy
Learning Objective: 9.5: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.
95. Albert Miller, VP of Production of a company that produces components for auto braking systems is examining the diameter of a specialized electrical wire produced with newly acquired machines in a new production line. For safety reasons, it is important that the variance in the diameter doesn’t exceed 0.15 inches. Albert knows that the variance of the other production lines is 0.15 and he wants to make sure the new machine also delivers products whose variance doesn’t exceed the safety limit. His staff randomly selects a sample of 25 wires and find out that the standard deviation of the sample is 0.42 inches. Assume that wire diameters are normally distributed. Using α = 0.10, the appropriate decision is ________.
a) increase the sample size
b) reduce the sample size
c) fail to reject the null hypothesis
d) maintain status quo
e) reject the null hypothesis
Response: See section 9.5 Testing Hypotheses about a Variance
Difficulty: Hard
Learning Objective: 9.5: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.
96. Discrete Components, Inc. manufactures a line of electrical resistors. Presently, the carbon composition line is producing 100-ohm resistors. The population variance of these resistors "must not exceed 4" to conform to industry standards. Periodically, the quality control inspectors check for conformity by randomly select 10 resistors from the line, and calculating the sample variance. The last sample had a variance of 4.36. Assume that the population is normally distributed. Using α = 0.05, the critical value of chi-square is _________________.
a) 18.31
b) 16.92
c) 3.94
d) 3.33
e) 19.82
Response: See section 9.5 Testing Hypotheses about a Variance
Difficulty: Medium
Learning Objective: 9.5: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.
97. Discrete Components, Inc. manufactures a line of electrical resistors. Presently, the carbon composition line is producing 100-ohm resistors. The population variance of these resistors "must not exceed 4" to conform to industry standards. Periodically, the quality control inspectors check for conformity by randomly select 10 resistors from the line, and calculating the sample variance. The last sample had a variance of 4.36. Assume that the population is normally distributed. Using α = 0.05, the observed value of chi-square is _________________.
a) 1.74
b) 1.94
c) 10.90
d) 9.81
e) 8.91
Response: See section 9.5 Testing Hypotheses about a Variance
Difficulty: Medium
Learning Objective: 9.5: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.
98. Discrete Components, Inc. manufactures a line of electrical resistors. Presently, the carbon composition line is producing 100-ohm resistors. The population variance of these resistors "must not exceed 4" to conform to industry standards. Periodically, the quality control inspectors check for conformity by randomly select 10 resistors from the line, and calculating the sample variance. The last sample had a variance of 4.36. Assume that the population is normally distributed. Using α = 0.05, the appropriate decision is _________________.
a) increase the sample size
b) reduce the sample size
c) reject the null hypothesis
d) fail to reject the null hypothesis
e) maintain status quo
Response: See section 9.5 Testing Hypotheses about a Variance
Difficulty: Hard
Learning Objective: 9.5: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.
99. David Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB. Based on a recent census of personnel, David knows that the variance of teller training time in the southeast region is 8, and he wonders if the variance in the southwest region is the same number. His staff randomly selected personnel files for 15 tellers in the southwest region, and determined that their mean training time was 25 hours and that the standard deviation was 4 hours. Assume that teller training time is normally distributed. Using α = 0.10, the null hypothesis is ________.
a) μ = 25
b) σ2 = 8
c) σ2 = 4
d) σ2 ≤ 8
e) s2 = 16
Response: See section 9.5 Testing Hypotheses about a Variance
Difficulty: Easy
Learning Objective: 9.5: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.
100. David Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB. Based on a recent census of personnel, David knows that the variance of teller training time in the southeast region is 8, and he wonders if the variance in the southwest region is the same number. His staff randomly selected personnel files for 15 tellers in the southwest region, and determined that their mean training time was 25 hours and that the standard deviation was 4 hours. Assume that teller training time is normally distributed. Using α = 0.10, the critical values of chi-square are ________.
a) 7.96 and 26.30
b) 6.57 and 23.68
c) -1.96 and 1.96
d) -1.645 and 1.645
e) -6.57 and 23.68
Response: See section 9.5 Testing Hypotheses about a Variance
Difficulty: Medium
Learning Objective: 9.5: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.
101. David Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB banks. Based on a recent census of personnel, David knows that the variance of teller training time in the southeast region is 8, and he wonders if the variance in the southwest region is the same number. His staff randomly selected personnel files for 15 tellers in the southwest region, and determined that their mean training time was 25 hours and that the standard deviation was 4 hours. Assume that teller training time is normally distributed. Using α = 0.10, the observed value of chi-square is ________.
a) 28.00
b) 30.00
c) 56.00
d) 60.00
e) 65.00
Response: See section 9.5 Testing Hypotheses about a Variance
Difficulty: Medium
Learning Objective: 9.5: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.
102. David Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB. Based on a recent census of personnel, David knows that the variance of teller training time in the southeast region is 8, and he wonders if the variance in the southwest region is the same number. His staff randomly selected personnel files for 15 tellers in the southwest region, and determined that their mean training time was 25 hours and that the standard deviation was 4 hours. Assume that teller training time is normally distributed. Using α = 0.10, the appropriate decision is ________.
a) increase the sample size
b) reduce the sample size
c) fail to reject the null hypothesis
d) maintain status quo
e) reject the null hypothesis
Response: See section 9.5 Testing Hypotheses about a Variance
Difficulty: Hard
Learning Objective: 9.5: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.
103. A company has a contract to supply specialized batteries to a manufacturer with a mean width of 54mm and a variance of 1.8 or less with an alpha of 0.05. The company randomly tests 20 of these batteries to ensure that they are meeting the requirements of the contract. What would be the null hypothesis each time the company conducts the test of the variances?
a) σ2 = 0.05
b) σ2 ≥ 1.34
c) s2 = 1.8
d) σ2 ≤ 1.8
e) μ = 54
Ans: d
Response: See section 9.5 Testing Hypotheses about a Variance
Difficulty: Easy
Learning Objective: 9.5: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.
104. A company has a contract to supply specialized batteries to a manufacturer with a mean width of 54mm and a variance of 1.8 or less with an alpha of 0.05. The company randomly tests 20 of these batteries to ensure that they are meeting the requirements of the contract. If the most recent test had a variance of 1.9, what would be the critical value of this chi-squared test?
a) 30.14
b) 32.85
c) 1.645
d) -30.14
e) -1.645
Ans: a
Response: See section 9.5 Testing Hypotheses about a Variance
Difficulty: Easy
Learning Objective: 9.5: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.
105. A company has a contract to supply specialized batteries to a manufacturer with a mean width of 54mm and a variance of 1.8 or less with an alpha of 0.05. The company randomly tests 20 of these batteries to ensure that they are meeting the requirements of the contract. If the most recent test had a variance of 1.9, what would be the observed chi-squared value?
a) 32.85
b) 17.91
c) 20.06
d) 30.14
e) 1.645
Ans: c
Response: See section 9.5 Testing Hypotheses about a Variance
Difficulty: Easy
Learning Objective: 9.5: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.
106. A company has a contract to supply specialized batteries to a manufacturer with a mean width of 54mm and a variance of 1.8 or less with an alpha of 0.05. The company randomly tests 20 of these batteries to ensure that they are meeting the requirements of the contract. If the most recent test had a variance of 1.9, what should the company do?
a) Continue production
b) Test the mean
c) Break the contract
d) Stop production to fix issues
e) Ask to revise the contract
Ans: a
Response: See section 9.5 Testing Hypotheses about a Variance
Difficulty: Hard
Learning Objective: 9.5: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.
107. A company has a contract to supply specialized batteries to a manufacturer with a mean width of 54mm and a standard deviation of 1.5 or less with an alpha of 0.10. The company randomly tests 25 of these batteries to ensure that they are meeting the requirements of the contract. If the most recent test had a standard deviation of 1.8 what would be the critical value of this chi-squared test?
a) -33.196
b) 36.415
c) 1.645
d) 33.196
e) 1.282
Ans: d
Response: See section 9.5 Testing Hypotheses about a Variance
Difficulty: Easy
Learning Objective: 9.5: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.
108. A company has a contract to supply specialized batteries to a manufacturer with a mean width of 54mm and a standard deviation of 1.5 or less with an alpha of 0.10. The company randomly tests 25 of these batteries to ensure that they are meeting the requirements of the contract. If the most recent test had a standard deviation of 1.8 what would be the observed chi-squared value?
a) 34.56
b) 36.42
c) 16.67
d) 33.20
e) -34.56
Ans: a
Response: See section 9.5 Testing Hypotheses about a Variance
Difficulty: Easy
Learning Objective: 9.5: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.
109. A company has a contract to supply specialized batteries to a manufacturer with a mean width of 54mm and a standard deviation of 1.5 or less with an alpha of 0.10. The company randomly tests 25 of these batteries to ensure that they are meeting the requirements of the contract. If the most recent test had a standard deviation of 1.8, what should the company do?
a) Continue production
b) Test the mean
c) Break the contract
d) Stop production to fix issues
e) Ask to revise the contract
Ans: d
Response: See section 9.5 Testing Hypotheses about a Variance
Difficulty: Hard
Learning Objective: 9.5: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.
110. The lifetime of a squirrel follows a normal distribution with mean μ months and a standard deviation =7 months. To test the alternative hypothesis that μ > 40, 25 squirrels are randomly selected. The null hypothesis is rejected when the sample mean is bigger than 43. Assuming that μ=45, the probability of type II error is approximately _________.
- 0.076
- 0.016
- 0.05
- 0.011
- 0.983
Response: See section 9.6 Solving for Type II Errors.
Difficulty: Hard
Learning Objective: 9.6: Solve for possible Type II errors when failing to reject the null hypothesis.
111. The lifetime of a squirrel follows a normal distribution with mean μ = 40 months and a standard deviation = 7 months. To test the hypothesis that μ > 40, 25 squirrels are randomly selected. Assuming that μ = 45, and α = 0.1, the probability of type II error is approximately
a) 0.076
b) 0.016
c) 0.05
d) 0.011
e) 0.983
Response: See section 9.6 Solving for Type II Errors.
Difficulty: Hard
Learning Objective: 9.6: Solve for possible Type II errors when failing to reject the null hypothesis.
112. The lifetime of a squirrel follows a normal distribution with mean μ = 40 months and a standard deviation = 7 months. To test the hypothesis that μ > 40, 25 squirrels are randomly selected. Assuming that μ = 45, and α = 0.1, the power is approximately
a) 0.076
b) 0.016
c) 0.05
d) 0.011
e) 0.989
Ans: e
Response: See section 9.6 Solving for Type II Errors.
Difficulty: Hard
Learning Objective: 9.6: Solve for possible Type II errors when failing to reject the null hypothesis.
113. A laptop battery lifespan follows a normal distribution with mean μ = 22 months and a standard deviation = 6 months. To test the alternative hypothesis that μ < 22 with α = .05, 36 laptop batteries are randomly selected. Assuming that μ = 21, the probability of type II error is approximately ________.
- -0.65
- 0.2422
- 0.64
- 0.7422
- 0.2508
Response: See section 9.6 Solving for Type II Errors.
Difficulty: Medium
Learning Objective: 9.6: Solve for possible Type II errors when failing to reject the null hypothesis.
114. A laptop battery lifespan follows a normal distribution with mean μ = 22 months and a standard deviation = 6 months. To test the alternative hypothesis that μ < 22 with α = .01, 36 laptop batteries are randomly selected. Assuming that μ = 24, the probability of type II error is approximately ________. a) -.01
b) 2.33
c) -4.33
d) 0.01
e) 0.00
Response: See section 9.6 Solving for Type II Errors.
Difficulty: Hard
Learning Objective: 9.6: Solve for possible Type II errors when failing to reject the null hypothesis.
115. A laptop battery lifespan follows a normal distribution with mean μ = 20 months and a standard deviation = 6 months. To test the alternative hypothesis that μ > 20 with α = .05, 36 laptop batteries are randomly selected. Assuming that μ = 21, the probability of type II error is approximately ________.
a) 0.00
b) 0.2595
c) 0.2036
d) 0.6449
e) 0.7405
Ans: e
Response: See section 9.6 Solving for Type II Errors.
Difficulty: Hard
Learning Objective: 9.6: Solve for possible Type II errors when failing to reject the null hypothesis.
116. A laptop battery lifespan follows a normal distribution with mean μ = 20 months and a standard deviation = 6 months. To test the alternative hypothesis that μ > 20 with α = .05, 36 laptop batteries are randomly selected. Assuming that μ = 21, the power of this is approximately ________.
a) 0.00
b) 0.2595
c) 0.2036
d) 0.6449
e) 0.7405
Ans: b
Response: See section 9.6 Solving for Type II Errors.
Difficulty: Hard
Learning Objective: 9.6: Solve for possible Type II errors when failing to reject the null hypothesis.
117. A recent survey suggests 30% of boat owners do not regularly use their boat after the second year of ownership. A local boat dealer wants to test the alternative hypothesis that p ≠ .30 with α = .05. He surveys 60 boat owners and finds 42% of the owners who have owned their boat for three years report they do not regularly use their boat. Assuming that p = .35, the probability of type II error is approximately ________.
a) 0.8542
b) 0.1458
c) 0.3577
d) 0.1423
e) 0.4965
Response: See section 9.6 Solving for Type II Errors.
Difficulty: Hard
Learning Objective: 9.6: Solve for possible Type II errors when failing to reject the null hypothesis.
118. A recent survey suggests 30% of boat owners do not regularly use their boat after the second year of ownership. A local boat dealer wants to test the alternative hypothesis that p > .30 with α = .05. He surveys 60 boat owners and finds 42% of the owners who have owned their boat for three years report they do not regularly use their boat. Assuming that p = .35, the probability of type II error is approximately ________.
a) 0.2211
b) 0.1421
c) 0.8579
d) 0.7789
e) 0.4965
Ans: d
Response: See section 9.6 Solving for Type II Errors.
Difficulty: Hard
Learning Objective: 9.6: Solve for possible Type II errors when failing to reject the null hypothesis.
119. A recent survey suggests 30% of boat owners do not regularly use their boat after the second year of ownership. A local boat dealer wants to test the alternative hypothesis that p > .30 with α = .05. He surveys 60 boat owners and finds 42% of the owners who have owned their boat for three years report they do not regularly use their boat. Assuming that p = .35, the power is approximately ________.
a) 0.2211
b) 0.1421
c) 0.8579
d) 0.7789
e) 0.4965
Ans: a
Response: See section 9.6 Solving for Type II Errors.
Difficulty: Hard
Learning Objective: 9.6: Solve for possible Type II errors when failing to reject the null hypothesis.
120. A car manufacturer looks at past sales and realizes that the most common car color is silver with 24% of purchasers selecting that color. The dealerships in one state believe that car purchasers in their area believe that the proportion of purchasers selecting silver is greater than 24%. Based on a survey of 84 car purchasers in the state, the dealerships find that 26% of them would select silver. If the true proportion selecting silver is 27%, what is the probability of the dealerships making a Type II error, given an alpha of 0.05?
a) 0.4587
b) 0.1154
c) 0.8322
d) 0.8423
e) 0.1678
Ans: c
Response: See section 9.6 Solving for Type II Errors.
Difficulty: Hard
Learning Objective: 9.6: Solve for possible Type II errors when failing to reject the null hypothesis.
121. A car manufacturer looks at past sales and realizes that the most common car color is silver with 24% of purchasers selecting that color. The dealerships in one state believe that car purchasers in their area believe that the proportion of purchasers selecting silver is greater than 24%. Based on a survey of 84 car purchasers in the state, the dealerships find that 26% of them would select silver. If the true proportion selecting silver is 27%, what is the power, given an alpha of 0.05?
a) 0.4587
b) 0.1154
c) 0.8322
d) 0.8423
e) 0.1678
Ans: e
Response: See section 9.6 Solving for Type II Errors.
Difficulty: Hard
Learning Objective: 9.6: Solve for possible Type II errors when failing to reject the null hypothesis.
122. Which of the following best describes a Type II error?
a) Rejecting the null when it is false
b) Failing to reject the null when it is false
c) Rejecting the null when it is true
d) Failing to reject the null when it is true
e) Rejecting the alternative when it is true
Ans: b
Response: See section 9.6 Solving for Type II Errors.
Difficulty: Hard
Learning Objective: 9.6: Solve for possible Type II errors when failing to reject the null hypothesis.
123. Which if the following would result in a higher probability of making a Type II error?
a) When the sample size is large
b) When the alpha is large
c) When the alternative value is far from the hypothesized value
d) When the alternative value is close to the hypothesized value
e) When the alternative value is under 10
Ans: d
Response: See section 9.6 Solving for Type II Errors.
Difficulty: Hard
Learning Objective: 9.6: Solve for possible Type II errors when failing to reject the null hypothesis.
124. Which of the following best describes the power?
a) Rejecting the null when it is false
b) Failing to reject the null when it is false
c) Rejecting the null when it is true
d) Failing to reject the null when it is true
e) Rejecting the alternative when it is true
Ans: a
Response: See section 9.6 Solving for Type II Errors.
Difficulty: Hard
Learning Objective: 9.6: Solve for possible Type II errors when failing to reject the null hypothesis.
Document Information
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Business Stats Contemporary Decision 10e | Test Bank by Ken Black
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