Estimation And Confidence Intervals Test Bank Answers Ch9

Basic Statistics for Business and Economics, 9e (Lind)

Chapter 9 Estimation and Confidence Intervals

1) A point estimate is a single value (point) computed from sample information and used to estimate a population value (parameter).

2) A point estimate is a range of values used to estimate a population parameter.

3) A confidence interval is a single value used to estimate a population parameter.

4) A confidence interval (also known as an interval estimate) is a range of values in which the population parameter is likely to occur.

5) A sample of 2,000 union members was selected and asked about their opinions regarding a proposed contract. A total of 1,600 members were in favor of it. A 95% confidence interval estimated that the population proportion was between 0.78 and 0.82. This indicates that about 80 out of 100 similarly constructed intervals would include the population proportion.

6) A confidence interval for a population proportion uses the uniform distribution (to approximate the binomial distribution).

7) The 95% confidence interval states that 95% of the sample means of a specified sample size selected from a population will lie within plus and minus 1.96 standard deviations of the hypothesized population mean.

8) One factor in determining the sample size for estimating the population mean is the degree of confidence selected. We logically choose relatively high levels of confidence such as 95% and 99%.

9) The population variation or dispersion has little or no effect in determining the sample size needed to estimate either a population mean or a population proportion.

10) To calculate the standard error of the mean, the standard deviation is divided by the sample size.

11) To calculate the required sample size to estimate a population mean, the standard deviation of the population must be estimated by either taking a pilot survey, using an estimate from a comparable study, or by using a range-based approach.

12) When using the t distribution to calculate a confidence interval (because the population standard deviation is not known), we assume that the population of interest is normal or approximately normal.

13) A z statistic is used for a problem involving any sample size and an unknown population standard deviation.

14) The mean number of travel days per year for salespeople employed by three hardware distributors needs to be estimated using a 90% level of confidence. For a small pilot study, the mean was 150 days and the standard deviation was 14 days. If the population mean is estimated within two days, how many salespeople should be sampled? (Please use Student's t distribution (Appendix B.5) at infinite degrees of freedom for three decimal accuracy of the required z value.)

A) 133

B) 452

C) 511

D) 2,100

15) A research firm needs to estimate within 3% the proportion of junior executives leaving large manufacturing companies within three years. A 95% level of confidence is to be used. Several years ago, a study revealed that 21% of junior executives left their company within three years. To update this study, how many junior executives should be surveyed?

A) 594

B) 612

C) 709

D) 897

16) There are 2,000 eligible voters in a precinct. A total of 500 voters are randomly selected and asked whether they plan to vote for the Democratic incumbent or the Republican challenger. Of the 500 surveyed, 350 said they would vote for the Democratic incumbent. Using the 99% level of confidence, what are the confidence limits for the proportion that plan to vote for the Democratic incumbent? (Please use Student's t distribution (Appendix B.5) at infinite degrees of freedom for three decimal accuracy of the required z value.)

A) 0.647 and 0.753

B) 0.612 and 0.712

C) 0.397 and 0.797

D) 0.826 and 0.926

17) A random sample of 85 supervisors revealed that they worked an average of 6.5 years before being promoted. The population standard deviation was 1.7 years. Using the 95% level of confidence, what is the confidence interval for the population mean?

A) 6.99 and 7.99

B) 4.15 and 7.15

C) 6.14 and 6.86

D) 6.49 and 7.49

18) The mean weight of trucks traveling on a particular section of I-475 is not known. A state highway inspector needs to estimate the population mean. He selects and weighs a random sample of 49 trucks. The mean weight of the 49 trucks was 15.8 tons. Assume for purposes of this problem that the population standard deviation is known, and it is 3.8 tons. What is the 95% confidence interval for the population mean?

A) 14.7 and 16.9

B) 13.2 and 17.6

C) 10.0 and 20.0

D) 16.1 and 18.1

19) A bank wishes to estimate the mean credit card balance owed by its customers. The population standard deviation is $300. The desired level of confidence is 98%, and the maximum allowable error is $75. How many customers should be sampled? (Please use Student's t distribution (Appendix B.5) at infinite degrees of freedom for three decimal accuracy of the required z value.)

A) 44

B) 212

C) 629

D) 87

20) Which of the following is a point estimate for the population mean (µ)?

A) σ

B) x/n

C)

D) s

21) Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile tires. The results showed that the mean tread life was 50,000 miles, with a standard deviation of 3,500 miles. What is the best estimate of the mean tread life in miles for the entire population of these tires?

A) 50,000

B) 3,500

C) 500

D) 35

22) Which of the following is the correct interpretation of a 96% confidence level?

A) There's a 96% chance that the given interval includes the true value of the population parameter.

B) Approximately 96 out of 100 such intervals would include the true value of the population parameter.

C) There's a 4% chance that the given interval does not include the true value of the population parameter.

D) The interval contains 96% of all sample means.

23) Which of the following statement(s) is/are correct about the t-distribution (assuming that the population of interest is normal, or nearly normal)?

A) The mean is zero.

B) Its shape is symmetric.

C) It approaches the standard normal distribution as the sample size increases

D) All apply.

24) What kind of distribution is the t-distribution?

A) Continuous

B) Discrete

C) Subjective

D) A z-distribution

25) How is the t-distribution similar to the standard normal z-distribution?

A) Both are discrete distributions.

B) Both are skewed distributions.

C) Both are families of distributions.

D) Both are continuous distributions.

26) A random sample of 20 items is selected (from a population with an unknown population standard deviation). When computing a confidence interval for the population mean, what number of degrees of freedom should be used to determine the appropriate t-value?

A) 20

B) 19

C) 21

D) 25

27) The t-distribution and z-distribution are the same in all of the following characteristics, except which one?

A) Continuous.

B) Symmetrical.

C) Bell-shaped.

D) Mean = 0, and standard deviation = 1.

28) Suppose 1,600 of 2,000 registered voters sampled said they planned to vote for the Republican candidate for president. Using the 95% level of confidence, what is the interval estimate for the population proportion (to the nearest 10th of a percent)?

A) 78.2% to 81.8%

B) 69.2% to 86.4%

C) 76.5% to 83.5%

D) 77.7% to 82.3%

29) Which of the following is NOT necessary to determine how large a sample to select from a population?

A) The level of confidence in estimating the population parameter

B) The size of the population

C) The maximum allowable error in estimating the population parameter

D) An estimate of the population variation

30) A sample mean is the best point estimate of the ________.

A) population standard deviation

B) population median

C) population mean

D) sample standard deviation

31) A sample standard deviation is the best point estimate of the ________.

A) population range

B) population skewness

C) population mode

D) population standard deviation

32) A confidence interval for a population mean estimates ________.

A) the population range

B) a likely interval for a population mean

C) likelihood or probability

D) the population standard deviation

33) Knowing the population standard deviation, a 95% confidence interval infers that the population mean ________.

A) is between 0 and 100%

B) is within ±1.96 standard deviations of the sample mean

C) is within ±1.96 standard errors of the sample mean

D) is too large

34) When a confidence interval for a population mean is constructed from sample data, ________.

A) we can conclude that the population mean is in the interval

B) we can conclude that the population mean is not in the interval

C) we can conclude, for an infinite number of samples and corresponding confidence intervals, that the population mean is in a stated percentage of the intervals

D) we cannot make any inferences

35) The Student's t-distribution has ________.

A) a mean of zero and a standard deviation of one

B) a mean of one and a standard deviation of one

C) a mean of zero and a standard deviation that depends on the sample size

D) a mean that depends on the sample size and a standard deviation of one

36)  Student's t-distribution is ________.

A) symmetrical

B) negatively skewed

C) positively skewed

D) a discrete probability distribution

37) When using Student's t-distribution to compute an interval estimate, ________.

A) we assume that the samples are collected from populations that are uniformly distributed

B) we use the population standard deviation

C) we use the z-distribution

D) we assume that the samples are collected from normally distributed populations

38) A random sample of 42 college graduates revealed that they worked an average of 5.5 years on the job before being promoted. The sample standard deviation was 1.1 years. Using the 99% level of confidence, what is the confidence interval for the population mean?

A) 5.04 and 5.96

B) 5.06 and 5.94

C) 2.67 and 8.33

D) 4.40 and 6.60

39) A local company wants to evaluate their quality of service by surveying their customers. Their budget limits the number of surveys to 100. What is their maximum error of the estimated mean quality for a 95% level of confidence and an estimated standard deviation of 5? (Please use Student's t distribution (Appendix B.5) at infinite degrees of freedom for three decimal accuracy of the required z value.)

A) 0.9604

B) 0.98

C) 1.96

D) 5%

40) A local retail company wants to estimate the mean amount spent by customers. Their store's budget limits the number of surveys to 225. What is their maximum error of the estimated mean amount spent for a 99% level of confidence and an estimated standard deviation of $10.00? (Please use Student's t distribution (Appendix B.5) at infinite degrees of freedom for three decimal accuracy of the required z value.)

A) $10.00

B) $1.00

C) 1%

D) $1.72

41) A university surveyed recent graduates of the English department for their starting salaries. Four hundred graduates returned the survey. The average salary was $25,000, with a standard deviation of $2,500. What is the best point estimate of the population mean?

A) $25,000

B) $2,500

C) $400

D) $62.5

42) A university surveyed recent graduates of the English department about their starting salaries. Four hundred graduates returned the survey. The average salary was $25,000. Assume for purposes of this problem that the population standard deviation is known, and it is $2,500. What is the 95% confidence interval for the mean salary of all graduates from the English department?

A) $22,500 and $27,500

B) $24,755 and $25,245

C) $24,988 and $25,012

D) $24,600 and $25,600

43) A university surveyed recent graduates of the English department about their starting salaries. Four hundred graduates returned the survey. The average salary was $25,000. Assume for purposes of this problem that the population standard deviation is known, and it is $2,500. A 95% confidence interval is constructed. What does the confidence interval mean?

A) The population mean is in the interval.

B) The population mean is not in the interval.

C) There is a 95% probability that the population parameter will lie within the interval constructed using the sample's data.

D) There is a 95% probability that the population parameter will not lie within the interval constructed using the sample's data.

44) A survey of an urban university (population of 25,450) showed that 870 of 1,100 students sampled supported a fee increase to fund improvements to the student recreation center. Using the 95% level of confidence, what is the confidence interval for the proportion of students supporting the fee increase? (Please use Student's t distribution (Appendix B.5) at infinite degrees of freedom for three decimal accuracy of the required z value.)

A) 0.767 and 0.815

B) 0.759 and 0.822

C) 0.771 and 0.811

D) 0.714 and 0.866

45) A survey of an urban university (population of 25,450) showed that 870 of 1,100 students sampled supported a fee increase to fund improvements to the student recreation center. Using the 99% level of confidence, what is the confidence interval for the proportion of students supporting the fee increase? (Please use Student's t distribution (Appendix B.5) at infinite degrees of freedom for three decimal accuracy of the required z value.)

A) 0.751 and 0.829

B) 0.759 and 0.823

C) 0.767 and 0.814

D) 0.771 and 0.811

46) University officials say that at least 70% of the voting student population supports a fee increase. If the 95% confidence interval estimating the proportion of students supporting the fee increase is (0.75; 0.85), what conclusion can be drawn?

A) Seventy percent is not in the interval, so another sample is needed.

B) Seventy percent is not in the interval, so assume it will not be supported.

C) The interval estimate is above 70%, so infer that it will be supported.

D) Since this was not based on the population, no conclusion can be drawn.

47) A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spent studying per week. Assuming a population standard deviation of six hours, what is the required sample size if the error should be less than a half hour with a 95% level of confidence?

A) 554

B) 130

C) 35

D) 393

48) A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spent studying per week. Assuming a population standard deviation of three hours, what is the required sample size if the error should be less than a half hour with a 99% level of confidence? (Please use Student's t distribution (Appendix B.5) at infinite degrees of freedom for three decimal accuracy of the required z value.)

A) 196

B) 239

C) 15

D) 16

49) A group of statistics students decided to conduct a survey at their university to estimate the average (mean) amount of time students spent studying per week. They sampled 554 students and found a mean of 22.3 hours per week. Assuming a population standard deviation of six hours, what is the confidence interval at the 95% level of confidence? (Please use Student's t distribution (Appendix B.5) at infinite degrees of freedom for three decimal accuracy of the required z value.)

A) 21.80 and 22.80

B) 16.3 and 28.3

C) 21.64 and 22.96

D) 20.22 and 22.0

50) A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spent studying per week. They sampled 240 students and found a mean of 22.3 hours per week. Assuming a population standard deviation of six hours, what is the confidence interval at the 95% level of confidence? (Please use Student's t distribution (Appendix B.5) at infinite degrees of freedom for three decimal accuracy of the required z value.)

A) 21.80 and 22.80

B) 16.3 and 28.3

C) 21.30 and 23.30

D) 20.22 and 22.0

51) A research firm wants to compute an interval estimate with 90% confidence for the mean time to complete an employment test. Assuming a population standard deviation of three hours, what is the required sample size if the error should be less than a half hour? (Please use Student's t distribution (Appendix B.5) at infinite degrees of freedom for three decimal accuracy of the required z value.)

A) 196

B) 98

C) 10

D) 16

52) A survey of 50 retail stores revealed that the average price of a microwave oven was $375, with a sample standard deviation of $20 (i.e. the population standard deviation was not known). Assuming the population is normally distributed, what is the 95% confidence interval to estimate the true cost of the microwave?

A) $323.40 to $426.60

B) $328.40 to $421.60

C) $350.80 to $395.80

D) $369.31 to $380.69

53) A survey of 50 retail stores revealed that the average price of a microwave oven was $375, with a sample standard deviation of $20 (i.e. the population standard deviation was not known). Assuming the population is normally distributed, what is the 99% confidence interval to estimate the true cost of the microwave?

A) $367.42 to $382.58

B) $315.00 to $415.00

C) $323.40 to $426.60

D) $335.82 to $414.28

54) A survey of 50 retail stores revealed that the average price of a microwave was $375, with a sample standard deviation of $20. If 90% and 95% confidence intervals were developed to estimate the true cost of the microwave, what similarities would they have?

A) Both have the same confidence level.

B) Both use the same t-statistic.

C) Both use the same z-statistic.

D) Both use the same point estimate of the population mean.

55) If 95% and 98% confidence intervals were calculated from the same sample data in order to estimate the true cost of an appliance with a known population standard deviation, what differences would there be between them?

A) The standard errors would be different.

B) The point estimates of the population mean would be different.

C) The sample sizes would be different.

D) The z-statistics would be different.

56) A student wanted to construct a 95% confidence interval for the mean age of students in her statistics class. She randomly selected nine students. Their average age was 19.1 years with a sample standard deviation of 1.5 years. What is the best point estimate for the population mean?

A) 2.1 years

B) 1.5 years

C) 19.1 years

D) 9 years

57) A student wanted to construct a 95% confidence interval for the mean age of students in her statistics class. She randomly selected nine students. Their mean age was 19.1 years, with a sample standard deviation of 1.5 years. What is the 95% confidence interval for the population mean?

A) 0.97 and 3.27

B) 15.64 and 22.56

C) 17.97 and 20.23

D) 17.95 and 20.25

58) A student wanted to construct a 99% confidence interval for the mean age of students in her statistics class. She randomly selected nine students. Their mean age was 19.1 years with a sample standard deviation of 1.5 years. What is the 99% confidence interval for the population mean?

A) 17.42 and 20.78

B) 17.48 and 20.72

C) 14.23 and 23.98

D) 0.44 and 3.80

59) A survey of 25 grocery stores produced the following sample statistics: 1.) mean price for a gallon of milk was $2.98, and 2.) a calculated standard error of $0.10. What is the 95% confidence interval to estimate the true cost of a gallon of milk?

A) $2.81 to $3.15

B) $2.94 to $3.02

C) $2.77 to $3.19

D) $2.95 to $3.01

60) A survey of 25 grocery stores produced the following sample statistics: 1.) mean price for a gallon of milk was $2.98, and 2.) a calculated standard error of $0.10. What is the 98% confidence interval to estimate the true cost of a gallon of milk?

A) $2.73 to $3.23

B) $2.85 to $3.11

C) $2.94 to $3.02

D) $2.95 to $3.01

61) A survey of 25 grocery stores produced the following sample statistics: 1.) mean price for a gallon of milk was $2.98, and 2.) a calculated standard error of $0.10. If 90% and 95% confidence intervals were developed from this sample data to estimate the true cost of a gallon of milk, what similarities would they have?

A) Both have the same confidence level.

B) Both use the same t-statistic.

C) Both use the same z-statistic.

D) Both use the same point estimate of the population mean.

62) A survey of an urban university (with a finite population of 25,450) showed that 750 of 1,100 students sampled attended a home football game during the season. Using the 99% level of confidence, what is the confidence interval for the proportion of students attending a football game? (Please use Student's t distribution (Appendix B.5) at infinite degrees of freedom for three decimal accuracy of the required z value.)

A) 0.7671 and 0.8143

B) 0.6550 and 0.7050

C) 0.6464 and 0.7172

D) 0.6805 and 0.6815

63) A survey of an urban university (with a finite population of 25,450) showed that 750 of 1,100 students sampled attended a home football game during the season. Using the 90% level of confidence, what is the confidence interval for the proportion of students attending a football game? (Please use Student's t distribution (Appendix B.5) at infinite degrees of freedom for three decimal accuracy of the required z value.)

A) 0.7510 and 0.8290

B) 0.6592 and 0.7044

C) 0.6659 and 0.6941

D) 0.6795 and 0.6805

64) A survey of households in a small town showed that in 850 of 1,200 sampled households, at least one member attended a town meeting during the year. Using the 99% level of confidence, what is the confidence interval for the proportion of households represented at a town meeting? (Please use Student's t distribution (Appendix B.5) at infinite degrees of freedom for three decimal accuracy of the required z value.)

A) 0.674 and 0.742

B) 0.655 and 0.705

C) 0.665 and 0.694

D) 0.679 and 0.680

65) A survey of households in a small town showed that in 500 of 1,200 sampled households, at least one member attended a town meeting during the year. Using the 95% level of confidence, what is the confidence interval for the proportion of households represented at a town meeting? (Please use Student's t distribution (Appendix B.5) at infinite degrees of freedom for three decimal accuracy of the required z value.)

A) 0.417 and 0.427

B) 0.389 and 0.445

C) 0.400 and 0.417

D) 0.417 and 0.445

66) A population has a known standard deviation of 25. A simple random sample of 49 items is taken from the selected population. The sample mean () is 300. What is the margin of error at the 95% confidence level?

A) ± 8

B) ± 93

C) ± 7

D) ± 0.8

67) As the sample size for a t-distribution increases, the differences between the t-distribution and the standard normal distribution ________.

A) are unchanged and remain the same

B) become smaller, as the t-distribution more closely approximates the standard normal distribution

C) become greater

D) are evident because the tails of the t-distribution become thicker

68) The z-score or z-value corresponding to a 95.34% confidence interval is ________.

A) 1.96

B) 1.65

C) 1.99

D) 1.68

69) Local government officials are interested in knowing if taxpayers are willing to support a school bond initiative that will require an increase in property taxes. A random sample of 750 likely voters was taken. Four hundred fifty of those sampled favored the school bond initiative. The 95% confidence interval for the true proportion of voters favoring the initiative is ________.

A) 0.541 and 0.639

B) 0.400 and 0.600

C) 0.500 and 0.700

D) 0.565 and 0.635

70) Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile tires. The sample mean tread wear was 50,000 miles, with a population standard deviation of 3,500 miles. What is the best estimate of the average tread life in miles for the entire population of these tires?

A) 50,000

B) 3,500

C) 500

D) 35