CHAPTER 9

STATISTICAL INFERENCE: HYPOTHESIS TESTING FOR SINGLE POPULATIONS

CHAPTER LEARNING OBJECTIVES

1. Develop both one- and two-tailed null and alternative 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. All statistical hypotheses consist of two parts, a null hypothesis and an alternative hypothesis. The null and alternative hypotheses are structured so that either one or the other is true but not both. In testing hypotheses, the researcher assumes that the null hypothesis is true. By examining the sampled data, the researcher either rejects or does not reject the null hypothesis. If the sample data are significantly in opposition to the null hypothesis, the researcher rejects the null hypothesis and accepts the alternative hypothesis by default.

Hypothesis tests can be one-tailed or two-tailed. Two-tailed tests always utilize = and ≠ in the null and alternative hypotheses. These tests are nondirectional in that significant deviations from the hypothesized value that are either greater than or less than the value are in rejection regions. The one-tailed test is directional, and the alternative hypothesis contains < or > signs. In these tests, only one end or tail of the distribution contains a rejection region. In a one-tailed test, the researcher is interested only in deviations from the hypothesized value that are either greater than or less than the value but not both.

Not all statistically significant outcomes of studies are important business outcomes. A substantive result is when the outcome of a statistical study produces results that are important to the decision maker.

When a business researcher reaches a decision about the null hypothesis, she either makes a correct decision or an error. If the null hypothesis is true, the researcher can make a Type I error by rejecting the null hypothesis. The probability of making a Type I error is alpha (α). Alpha is usually set by the researcher when establishing the hypotheses. Another expression sometimes used for the value of α is level of significance.

2. Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic. Included in this chapter were hypothesis tests for a single mean when σ is known and when σ is unknown, a test of a single population proportion, and a test for a population variance. Three different analytic approaches were presented: (1) the standard method, (2) the p value method, and (3) the critical value method.

3. Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic. Included in this chapter were hypothesis tests for a single mean when σ is known and when σ is unknown, a test of a single population proportion, and a test for a population variance. Three different analytic approaches were presented: (1) the standard method, (2) the p value method, and (3) the critical value method.

4. Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic. Included in this chapter were hypothesis tests for a single mean when σ is known and when σ is unknown, a test of a single population proportion, and a test for a population variance. Three different analytic approaches were presented: (1) the standard method, (2) the p value method, and (3) the critical value method.

5. Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic. Included in this chapter were hypothesis tests for a single mean when σ is known and when σ is unknown, a test of a single population proportion, and a test for a population variance. Three different analytic approaches were presented: (1) the standard method, (2) the p value method, and (3) the critical value method.

6. Solve for possible Type II errors when failing to reject the null hypothesis. If the null hypothesis is false and the researcher fails to reject it, a Type II error is committed. Beta (β) is the probability of committing a Type II error. Type II errors must be computed from the hypothesized value of the parameter, α, and a specific alternative value of the parameter being examined. As many possible Type II errors in a problem exist as there are possible alternative statistical values.

If a null hypothesis is true and the researcher fails to reject it, no error is committed, and the researcher makes a correct decision. Similarly, if a null hypothesis is false and it is rejected, no error is committed. Power (1 – β) is the probability of a statistical test rejecting the null hypothesis when the null hypothesis is false.

An operating characteristic (OC) curve is a graphical depiction of values of β that can occur as various values of the alternative values of the parameter are explored. This graph can be studied to determine what happens to β as one moves away from the value of the null hypothesis. A power curve is used in conjunction with an OC curve. The power curve is a graphical depiction of the values of power as alternative values of the parameter are examined. The researcher can view the increase in power as values of the parameter diverge from the value of the null hypothesis.

TRUE-FALSE STATEMENTS

1. Hypotheses are tentative explanations of a principle operating in nature.

Difficulty: Easy

Learning Objective: Develop both one- and two-tailed null and alternative 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.

Section Reference: 9.1 Introduction to Hypothesis Testing

Bloom’s: Knowledge

AACSB: Reflective Thinking

2. The first step in testing a hypothesis is to establish a true null hypothesis and a false alternative hypothesis.

Difficulty: Easy

Learning Objective: Develop both one- and two-tailed null and alternative 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.

Section Reference: 9.1 Introduction to Hypothesis Testing

Bloom’s: Comprehension

AACSB: Reflective Thinking

3. In testing hypotheses, the researcher initially assumes that the alternative hypothesis is true and uses the sample data to reject it.

Difficulty: Easy

Learning Objective: Develop both one- and two-tailed null and alternative 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.

Section Reference: 9.1 Introduction to Hypothesis Testing

Bloom’s: Comprehension

AACSB: Reflective Thinking

4. The null and the alternative hypotheses must be mutually exclusive and collectively exhaustive.

Difficulty: Medium

Learning Objective: Develop both one- and two-tailed null and alternative 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.

Section Reference: 9.1 Introduction to Hypothesis Testing

Bloom’s: Comprehension

AACSB: Reflective Thinking

5. Generally speaking, the hypotheses that business researchers want to prove are stated in the alternative hypothesis.

Difficulty: Medium

Learning Objective: Develop both one- and two-tailed null and alternative 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.

Section Reference: 9.1 Introduction to Hypothesis Testing

Bloom’s: Comprehension

AACSB: Reflective Thinking

6. The probability of committing a Type I error is called the power of the test.

Difficulty: Medium

Learning Objective: Develop both one- and two-tailed null and alternative 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.

Section Reference: 9.1 Introduction to Hypothesis Testing

Bloom’s: Knowledge

AACSB: Reflective Thinking

7. When a true null hypothesis is rejected, the researcher has made a Type I error.

Difficulty: Medium

Learning Objective: Develop both one- and two-tailed null and alternative 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.

Section Reference: 9.1 Introduction to Hypothesis Testing

Bloom’s: Evaluation

AACSB: Reflective Thinking

8. When a false null hypothesis is rejected, the researcher has made a Type II error.

Difficulty: Medium

Learning Objective: Develop both one- and two-tailed null and alternative 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.

Section Reference: 9.1 Introduction to Hypothesis Testing

Bloom’s: Evaluation

AACSB: Reflective Thinking

9. When a researcher fails to reject a false null hypothesis, a Type II error has been committed.

Difficulty: Medium

Learning Objective: Develop both one- and two-tailed null and alternative 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.

Section Reference: 9.1 Introduction to Hypothesis Testing

Bloom’s: Evaluation

AACSB: Reflective Thinking

10. Power is equal to (1 –β), the probability of a test rejecting the null hypothesis that is indeed false.

Difficulty: Medium

Learning Objective: Develop both one- and two-tailed null and alternative 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.

Section Reference: 9.1 Introduction to Hypothesis Testing

Bloom’s: Application

AACSB: Reflective Thinking

11. The rejection region for a hypothesis test becomes smaller if the level of significance is changed from 0.01 to 0.05.

Difficulty: Hard

Learning Objective: Develop both one- and two-tailed null and alternative 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.

Section Reference: 9.1 Introduction to Hypothesis Testing

Bloom’s: Analysis

AACSB: Reflective Thinking

12. Whenever hypotheses are established such that the alternative hypothesis is ">", then this would be a two-tailed test.

Difficulty: Medium

Learning Objective: Develop both one- and two-tailed null and alternative 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.

Section Reference: 9.1 Introduction to Hypothesis Testing

Bloom’s: Application

AACSB: Reflective Thinking

13. Whenever hypotheses are established such that the alternative hypothesis is "not equal to", the hypothesis test would be a two-tailed test.

Difficulty: Medium

Learning Objective: Develop both one- and two-tailed null and alternative 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.

Section Reference: 9.1 Introduction to Hypothesis Testing

Bloom’s: Application

AACSB: Reflective Thinking

14. The rejection and nonrejection regions are divided by a point called the critical value.

Difficulty: Medium

Learning Objective: Develop both one- and two-tailed null and alternative 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.

Section Reference: 9.1 Introduction to Hypothesis Testing

Bloom’s: Knowledge

AACSB: Reflective Thinking

15. If the researcher computes the probability of the calculated statistic and compares it to alpha, the level of significance to reach a decision, the researcher is using the p-value method for testing the hypotheses.

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.

Section Reference: 9.2 Testing Hypotheses about a Population Mean Using the z Statistic (σ Known)

Bloom’s: Comprehension

AACSB: Reflective Thinking

16. 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.

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.

Section Reference: 9.2 Testing Hypotheses about a Population Mean Using the z Statistic (σ Known)

Bloom’s: Application

AACSB: Reflective Thinking

MULTIPLE CHOICE QUESTIONS

17. Consider the following null and alternative hypotheses:

Ho: µ ≤ 67

Ha: µ > 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

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.

Section Reference: 9.2 Testing Hypotheses about a Population Mean Using the z Statistic (σ Known)

Bloom’s: Application

AACSB: Reflective Thinking

18. Consider the following null and alternative hypotheses.

Ho: µ ≥ 67

Ha: µ < 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

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.

Section Reference: 9.2 Testing Hypotheses about a Population Mean Using the z Statistic (σ Known)

Bloom’s: Application

AACSB: Reflective Thinking

19. Consider the following null and alternative hypotheses.

Ho: µ = 67

Ha: µ ≠ 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

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.

Section Reference: 9.2 Testing Hypotheses about a Population Mean Using the z Statistic (σ Known)

Bloom’s: Application

AACSB: Reflective Thinking

20. Suppose the alternative hypothesis in a hypothesis test is: "the population mean is less than 60". If the sample size is 50 and alpha =.05, the critical value of z is ___.

a) 1.645

b) –1.645

c) 1.96

d) –1.96

e) 2.05

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.

Section Reference: 9.2 Testing Hypotheses about a Population Mean Using the z Statistic (σ Known)

Bloom’s: Application

AACSB: Analytic

21. Suppose the alternative hypothesis in a hypothesis test is "the population mean is greater than 60". If the sample size is 80 and alpha = .01, the critical value of z is ___.

a) 2.575

b) –2.575

c) 2.33

d) –2.33

e) 2.45

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.

Section Reference: 9.2 Testing Hypotheses about a Population Mean Using the z Statistic (σ Known)

Bloom’s: Application

AACSB: Analytic

22. In a two-tailed hypothesis about a population mean with a sample size of 100 and alpha = 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 < –1.645 and z > 1.645

e) z < –2.33 and z > 2.33

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.

Section Reference: 9.2 Testing Hypotheses about a Population Mean Using the z Statistic (σ Known)

Bloom’s: Application

AACSB: Analytic

23. In a two-tailed hypothesis about a population mean with a sample size of 100 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

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.

Section Reference: 9.2 Testing Hypotheses about a Population Mean Using the z Statistic (σ Known)

Bloom’s: Application

AACSB: Analytic

24. Suppose you are testing the null hypothesis that a population mean is less than or equal to 80, against the alternative hypothesis that the population mean is greater than 80. If the sample size is 49 and alpha = .10, the critical value of z is ___.

a) 1.645

b) –1.645

c) 1.28

d) –1.28

e) 2.33

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.

Section Reference: 9.2 Testing Hypotheses about a Population Mean Using the z Statistic (σ Known)

Bloom’s: Application

AACSB: Analytic

25. Suppose you are testing the null hypothesis that a population mean is less than or equal to 80, against the alternative hypothesis that the population mean is greater than 80. The sample size is 49 and alpha =.05. If the sample mean is 84 and the population standard deviation is 14, the observed z value is ___.

a) 2

b) –2

c) 14

d) –14

e) 49

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.

Section Reference: 9.2 Testing Hypotheses about a Population Mean Using the z Statistic (σ Known)

Bloom’s: Application

AACSB: Analytic

26. 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

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.

Section Reference: 9.2 Testing Hypotheses about a Population Mean Using the z Statistic (σ Known)

Bloom’s: Application

AACSB: Analytic

27. A researcher is testing a hypothesis of a single mean. The critical z value for α = .05 and 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) not reject

c) redefine

d) change the alternate hypothesis into

e) restate

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.

Section Reference: 9.2 Testing Hypotheses about a Population Mean Using the z Statistic (σ Known)

Bloom’s: Analysis

AACSB: Analytic

28. A researcher is testing a hypothesis of a single mean. The critical z value for α = .05 and 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) not reject

c) redefine

d) change the alternate hypothesis into

e) restate

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.

Section Reference: 9.2 Testing Hypotheses about a Population Mean Using the z Statistic (σ Known)

Bloom’s: Analysis

AACSB: Analytic

29. A researcher is testing a hypothesis of a single mean. The critical z value for α = .05 and 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) not reject

c) redefine

d) change the alternate hypothesis into

e) restate

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.

Section Reference: 9.2 Testing Hypotheses about a Population Mean Using the z Statistic (σ Known)

Bloom’s: Analysis

AACSB: Analytic

30. A researcher is testing a hypothesis of a single mean. The critical z value for α = .05 and 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) not reject

c) redefine

d) change the alternate hypothesis into

e) restate

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.

Section Reference: 9.2 Testing Hypotheses about a Population Mean Using the z Statistic (σ Known)

Bloom’s: Analysis

AACSB: Analytic

31. A company produces an item that is supposed to have a six centimetre hole punched in the centre. A quality control inspector is concerned that the machine which punches the hole is "out-of-control" (hole is too large or too small). In an effort to test this, the inspector is going to gather a sample punched by the machine and measure the diameter of the hole. The alternative hypothesis used to statistical test to determine if the machine is out-of-control is

a) the mean diameter is > 6 centimetres.

b) the mean diameter is < 6 centimetres.

c) the mean diameter is = 6 centimetres.

d) the mean diameter is ≠ 6 centimetres.

e) the mean diameter is ≥ 6 centimetres.

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.

Section Reference: 9.2 Testing Hypotheses about a Population Mean Using the z Statistic (σ Known)

Bloom’s: Application

AACSB: Reflective Thinking

32. Jennifer Cantu, VP of Customer Services at Tri-City 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

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with a known population standard deviation using the z statistic.

Section Reference: 9.2 Testing Hypotheses about a Population Mean Using the z Statistic (σ Known)

Bloom’s: Application

AACSB: Reflective Thinking

33. 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

Difficulty: Easy

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.

Section Reference: 9.3 Testing Hypotheses about a Population Mean using the t Statistic (σ Unknown)

Bloom’s: Application

AACSB: Analytic

34. 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

Difficulty: Easy

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.

Section Reference: 9.3 Testing Hypotheses about a Population Mean using the t Statistic (σ Unknown)

Bloom’s: Application

AACSB: Analytic

35. 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 table "t" value for this problem is ___.

a) 1.318

b) 1.711

c) 2.492

d) 2.797

e) 3.227

Difficulty: Easy

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.

Section Reference: 9.3 Testing Hypotheses about a Population Mean using the t Statistic (σ Unknown)

Bloom’s: Application

AACSB: Analytic

36. 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

Difficulty: Easy

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.

Section Reference: 9.3 Testing Hypotheses about a Population Mean using the t Statistic (σ Unknown)

Bloom’s: Application

AACSB: Analytic

37. In performing a hypothesis test where the null hypothesis is that the population mean is 6.9 against the alternative hypothesis that the population mean is not equal to 6.9, a random sample of 16 items is selected. The sample mean is 7.1 and the sample standard deviation is 2.4. It can be assumed that the population is normally distributed. The observed "t" value for this problem is ___.

a) 0.05

b) 0.20

c) 0.33

d) 1.33

e) 1.43

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.

Section Reference: 9.3 Testing Hypotheses about a Population Mean using the t Statistic (σ Unknown)

Bloom’s: Application

AACSB: Analytic

38. In performing a hypothesis test where the null hypothesis is that the population mean is 6.9 against the alternative hypothesis that the population mean is not equal to 6.9, a random sample of 16 items is selected. The sample mean is 7.1 and the sample standard deviation is 2.4. It can be assumed that the population is normally distributed. The level of significance is selected as 0.05. The table "t" value for this problem is ___.

a) 1.753

b) 2.947

c) 2.120

d) 2.131

e) 2.311

Difficulty: Easy

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.

Section Reference: 9.3 Testing Hypotheses about a Population Mean using the t Statistic (σ Unknown)

Bloom’s: Application

AACSB: Analytic

39. In performing a hypothesis test where the null hypothesis is that the population mean is 6.9 against the alternative hypothesis that the population mean is not equal to 6.9, a random sample of 16 items is selected. The sample mean is 7.1 and the sample standard deviation is 2.4. It can be assumed that the population is normally distributed. The level of significance is selected as 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

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.

Section Reference: 9.3 Testing Hypotheses about a Population Mean using the t Statistic (σ Unknown)

Bloom’s: Application

AACSB: Analytic

40. The diameter of 3.5 centimetre discs is normally distributed. Periodically, quality control inspectors at Winnipeg Discs randomly select a sample of 16 discs. If the mean diameter of the discs is too large or too small the disc punch is shut down for adjustment; otherwise, the punching process continues. The last sample showed a mean and standard deviation of 3.49 and 0.08 centimetres, respectively. Using α = 0.05, 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

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.

Section Reference: 9.3 Testing Hypotheses about a Population Mean using the t Statistic (σ Unknown)

Bloom’s: Analysis

AACSB: Analytic

41. The diameter of 3.5 centimetre discs is normally distributed. Periodically, quality control inspectors at Winnipeg Discs randomly select a sample of 16 discs. If the mean diameter of the discs is too large or too small the disc punch is shut down for adjustment; otherwise, the punching process continues. The null hypothesis is ___.

a) n ≠ 16

b) n = 16

c) μ = 3.5

d) μ ≠ 3.5

e) μ ≥ 3.5

Difficulty: Easy

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.

Section Reference: 9.3 Testing Hypotheses about a Population Mean using the t Statistic (σ Unknown)

Bloom’s: Application

AACSB: Reflective Thinking

42. The diameter of 3.5 centimetre discs is normally distributed. Periodically, quality control inspectors at Winnipeg Discs randomly select a sample of 16 discs. If the mean diameter of the discs is too large or too small the disc punch is shut down for adjustment; otherwise, the punching process continues. The last sample showed a mean and standard deviation of 3.49 and 0.08 centimetres, respectively. Using α = 0.05, the appropriate decision is ___.

a) reject the null hypothesis and shut down the punch

b) reject the null hypothesis and do not shut down the punch

c) do not reject the null hypothesis and shut down the punch

d) do not reject the null hypothesis and do not shut down the punch

e) do nothing

Difficulty: Hard

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.

Section Reference: 9.3 Testing Hypotheses about a Population Mean using the t Statistic (σ Unknown)

Bloom’s: Analysis

AACSB: Analytic

43. The diameter of 3.5 centimetre discs is normally distributed. Periodically, quality control inspectors at Winnipeg Discs randomly select a sample of 16 discs. If the mean diameter of the discs is too large or too small the disc punch is shut down for adjustment; otherwise, the punching process continues. The last sample showed a mean and standard deviation of 3.55 and 0.08 centimetres, respectively. Using α = 0.05, the appropriate decision is ___.

a) reject the null hypothesis and shut down the punch

b) reject the null hypothesis and do not shut down the punch

c) do not reject the null hypothesis and shut down the punch

d) do not reject the null hypothesis and do not shut down the punch

e) do nothing

Difficulty: Hard

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.

Section Reference: 9.3 Testing Hypotheses about a Population Mean using the t Statistic (σ Unknown)

Bloom’s: Analysis

AACSB: Analytic

44. In performing hypothesis tests about the population mean, the population standard deviation should be used if it is known. If it is not known, which of the following statistical test should be used?

a) z test of a population mean

b) t test of a population mean

c) z test of a population proportion

d) χ² test of a population variance

e) t test of a population proportion

Difficulty: Easy

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.

Section Reference: 9.3 Testing Hypotheses about a Population Mean using the t Statistic (σ Unknown)

Bloom’s: Knowledge

AACSB: Reflective Thinking

45. In performing hypothesis tests about the population mean, the population standard deviation should be used if it is known. If it is not known, a t test can be used to test the mean if ___.

a) the sample size is at least thirty

b) the sample is random

c) the population mean is known

d) the population is normally distributed

e) the population is chi-square distributed

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.

Section Reference: 9.3 Testing Hypotheses about a Population Mean using the t Statistic (σ Unknown)

Bloom’s: Comprehension

AACSB: Reflective Thinking

46. 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 t value is ___.

a) –0.22

b) 0.22

c) 1.33

d) 8.08

e) 7.58

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.

Section Reference: 9.3 Testing Hypotheses about a Population Mean using the t Statistic (σ Unknown)

Bloom’s: Analysis

AACSB: Analytic

47. Consider the following null and alternative hypotheses:

Ho: p ≤ 0.16

Ha: p > 0.16

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

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.

Section Reference: 9.4 Testing Hypotheses about a Proportion

Bloom’s: Application

AACSB: Reflective Thinking

48. Consider the following null and alternative hypotheses:

Ho: p ≥ 0.16

Ha: p < 0.16

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

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.

Section Reference: 9.4 Testing Hypotheses about a Proportion

Bloom’s: Application

AACSB: reflective Thinking

49. Consider the following null and alternative hypotheses:

Ho: p = 0.16

Ha: p ≠ 0.16

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

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.

Section Reference: 9.4 Testing Hypotheses about a Proportion

Bloom’s: Application

AACSB: Reflective Thinking

50. A political scientist wants to prove that a candidate is currently carrying more than 60% of the vote in the riding. She has her assistants randomly sample 200 eligible voters in the riding 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

Difficulty: Easy

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.

Section Reference: 9.4 Testing Hypotheses about a Proportion

Bloom’s: Application

AACSB: Analytic

51. 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 purchased this company's brand of the product. 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

Difficulty: Easy

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.

Section Reference: 9.4 Testing Hypotheses about a Proportion

Bloom’s: Application

AACSB: Reflective Thinking

52. 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 purchased this company's brand of the product. 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

Difficulty: Easy

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.

Section Reference: 9.4 Testing Hypotheses about a Proportion

Bloom’s: Application

AACSB: Analytic

53. 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 purchased this company's brand of the product. 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

Difficulty: Easy

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.

Section Reference: 9.4 Testing Hypotheses about a Proportion

Bloom’s: Application

AACSB: Reflective Thinking

54. Ophelia O'Brien, VP of Consumer Credit of Credit First Banks (CFB), monitors the default rate on personal loans at the CFB 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

Difficulty: Easy

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.

Section Reference: 9.4 Testing Hypotheses about a Proportion

Bloom’s: Application

AACSB: Reflective Thinking

55. Ophelia O'Brien, VP of Consumer Credit of Credit First Banks (CFB), monitors the default rate on personal loans at the CFB 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

Difficulty: Easy

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.

Section Reference: 9.4 Testing Hypotheses about a Proportion

Bloom’s: Application

AACSB: Analytic

56. Ophelia O'Brien, VP of Consumer Credit of Credit First Banks (CFB), monitors the default rate on personal loans at the CFB 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

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.

Section Reference: 9.4 Testing Hypotheses about a Proportion

Bloom’s: Application

AACSB: Analytic

57. Ophelia O'Brien, VP of Consumer Credit of Credit First Banks (CFB), monitors the default rate on personal loans at the CFB 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 ___.

a) reduce the sample size

b) increase the sample size

c) reject the null hypothesis

d) do not reject the null hypothesis

e) do nothing

Difficulty: Hard

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.

Section Reference: 9.4 Testing Hypotheses about a Proportion

Bloom’s: Analysis

AACSB: Analytic

58. Ophelia O'Brien, VP of Consumer Credit of Credit First Banks (CFB), monitors the default rate on personal loans at the CFB 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 ___.

a) reduce the sample size

b) increase the sample size

c) reject the null hypothesis

d) do not reject the null hypothesis

e) do nothing

Difficulty: Hard

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.

Section Reference: 9.4 Testing Hypotheses about a Proportion

Bloom’s: Analysis

AACSB: Analytic

59. 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

Difficulty: Easy

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.

Section Reference: 9.4 Testing Hypotheses about a Proportion

Bloom’s: Application

AACSB: Reflective Thinking

60. 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 ___.

a) do not reject the null hypothesis

b) reject the null hypothesis

c) reduce the sample size

d) increase the sample size

e) do nothing

Difficulty: Hard

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.

Section Reference: 9.4 Testing Hypotheses about a Proportion

Bloom’s: Analysis

AACSB: Analytic

61. 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 ___.

a) do not reject the null hypothesis

b) reject the null hypothesis

c) reduce the sample size

d) increase the sample size

e) maintain status quo

Difficulty: Hard

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.

Section Reference: 9.4 Testing Hypotheses about a Proportion

Bloom’s: Analysis

AACSB: Analytic

62. Elwin Osbourne, CIO at GFS, Inc., suspects that at least 25% of email messages sent by GFS employees are not business related. A random sample of 300 email 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

Difficulty: Easy

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.

Section Reference: 9.4 Testing Hypotheses about a Proportion

Bloom’s: Application

AACSB: Reflective Thinking

63. Elwin Osbourne, CIO at GFS, Inc., suspects that at least 25% of email messages sent by GFS employees are not business related. A random sample of 300 email 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 __.

a) increase the sample size

b) gather more data

c) reject the null hypothesis

d) do not reject the null hypothesis

e) maintain status quo

Difficulty: Easy

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.

Section Reference: 9.4 Testing Hypotheses about a Proportion

Bloom’s: Analysis

AACSB: Analytic

64. Elwin Osbourne, CIO at GFS, Inc., suspects that at least 25% of email messages sent by GFS employees are not business related. A random sample of 300 email 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 ___.

a) increase the sample size

b) gather more data

c) maintain status quo

d) do not reject the null hypothesis

e) reject the null hypothesis

Difficulty: Easy

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.

Section Reference: 9.4 Testing Hypotheses about a Proportion

Bloom’s: Analysis

AACSB: Analytic

65. 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 null hypothesis is ___.

a) μ = 100

b) σ ≤ 10

c) s² ≥ 4

d) σ² ≤ 4

e) n = 100

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.

Section Reference: 9.5 Testing Hypotheses about a Variance

Bloom’s: Application

AACSB: Reflective Thinking

66. 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

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.

Section Reference: 9.5 Testing Hypotheses about a Variance

Bloom’s: Application

AACSB: Analytic

67. 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

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.

Section Reference: 9.5 Testing Hypotheses about a Variance

Bloom’s: Application

AACSB: Analytic

68. 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) do not reject the null hypothesis

e) maintain status quo

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.

Section Reference: 9.5 Testing Hypotheses about a Variance

Bloom’s: Analysis

AACSB: Analytic

69. David Desreumaux, VP of Human Resources of Maritime Boat Manufacturing (MBM), is reviewing the employee training programs of MBM factories. Based on a recent census of personnel, David knows that the variance of worker training time in New Brunswick is 8, and he wonders if the variance in Nova Scotia is the same number. His staff randomly selected personnel files for 15 workers in Nova Scotia, and determined that their mean training time was 25 hours and that the standard deviation was 4 hours. Assume that worker training time is normally distributed in the population. Using α = 0.10, the null hypothesis is ___.

a) μ = 25

b) σ² = 8

c) σ² = 4

d) σ² ≤ 8

e) s² = 16

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.

Section Reference: 9.5 Testing Hypotheses about a Variance

Bloom’s: Application

AACSB: Reflective Thinking

70. David Desreumaux, VP of Human Resources of Maritime Boat Manufacturing (MBM), is reviewing the employee training programs of MBM factories. Based on a recent census of personnel, David knows that the variance of worker training time in New Brunswick is 8, and he wonders if the variance in Nova Scotia is the same number. His staff randomly selected personnel files for 15 workers in Nova Scotia, and determined that their mean training time was 25 hours and that the standard deviation was 4 hours. Assume that worker training time is normally distributed in the population. 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

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.

Section Reference: 9.5 Testing Hypotheses about a Variance

Bloom’s: Application

AACSB: Analytic

71. David Desreumaux, VP of Human Resources of Maritime Boat Manufacturing (MBM), is reviewing the employee training programs of MBM factories. Based on a recent census of personnel, David knows that the variance of worker training time in New Brunswick is 8, and he wonders if the variance in Nova Scotia is the same number. His staff randomly selected personnel files for 15 workers in Nova Scotia, and determined that their mean training time was 25 hours and that the standard deviation was 4 hours. Assume that worker training time is normally distributed in the population. 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

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.

Section Reference: 9.5 Testing Hypotheses about a Variance

Bloom’s: Application

AACSB: Analytic

72. David Desreumaux, VP of Human Resources of Maritime Boat Manufacturing (MBM), is reviewing the employee training programs of MBM factories. Based on a recent census of personnel, David knows that the variance of worker training time in New Brunswick is 8, and he wonders if the variance in Nova Scotia is the same number. His staff randomly selected personnel files for 15 workers in Nova Scotia, and determined that their mean training time was 25 hours and that the standard deviation was 4 hours. Assume that worker training time is normally distributed in the population. Using α = 0.10, the appropriate decision is ___.

a) increase the sample size

b) reduce the sample size

c) do not reject the null hypothesis

d) maintain status quo

e) reject the null hypothesis

Difficulty: Medium

Learning Objective: Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.

Section Reference: 9.5 Testing Hypotheses about a Variance

Bloom’s: Analysis

AACSB: Analytic

73. A null hypothesis is p > 0.65. To test this hypothesis, a sample of 400 is taken and alpha is set at 0.05. If the true proportion is p = 0.60, what is the probability of a Type II error?

a) 0.17

b) 0.45

c) 0.95

d) 0.67

e) 0.33

Difficulty: Hard

Learning Objective: Solve for possible Type II errors when failing to reject the null hypothesis.

Section Reference: 9.6 Solving for Type II Errors

Bloom’s: Analysis

AACSB: Analytic

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