Questions 1: Select the best answer to each question. Note that a question and its answers may be split across a page break, so be sure that you have seen the entire question and all the answers before choosing an answer.
1. A woman and her son are debating about the average length of a preacher's sermons on Sunday morning. Despite the mother's arguments, the son thinks that the sermons are more than twenty minutes. For one year, he has randomly selected 12 Sundays and found an average time of 26.42 minutes with a standard deviation of 6.69 minutes. Assuming that the population is normally distributed and using a 0.05 level of significance, he wishes to determine whether he is correct in thinking that the average length of sermons is more than 20 minutes. What is the test statistic?
A. 0.95 B. 6.69 C. -3.32 D. 3.32
2. If the level of significance (α) is 0.005 in a two-tail test, how large is the nonrejection region under the curve of the t distribution?
A. 0.005 B. 0.995 C. 0.9975 D. 0.050
3. A federal auditor for nationally chartered banks, from a random sample of 100 accounts, found that the average demand deposit balance at the First National Bank of Arkansas was $549.82. If the auditor needed a point estimate for the population mean for all accounts at this bank, what should he use?
A. There's no acceptable value available. B. The average of $549.82 for this sample C. The auditor should survey the total of all accounts and determine the mean. D. The average of $54.98 for this sample
4. In the statement of a null hypothesis, you would likely find which of the following terms? A. = B. >C. =?
D. <
5. A random sample of 10 employees is selected from a large firm. For the 10 employees, the number of days each was absent during the past month was found to be 0, 2, 4, 2, 5, 1, 7, 3, 2, and 4. Of the following values, which would you use as the point estimate for the average number of days absent for all the firm's employees?
A. 4 B. 2.5 C. 30 D. 3
6. What is the rejection region for a two-tailed test when α = 0.05? A. |z| > 1.645 B. |z | > 2.575 C. |z | > 1.96
D. z> 2.575
7. A researcher wants to carry out a hypothesis test involving the mean for a sample of n = 20. While the true value of the population standard deviation is unknown, the researcher is reasonably sure that the population is normally distributed. Given this information, which of the following statements would be correct?
A. The researcher should use the z-test because the sample size is less than 30. B. The t-test should be used because the sample size is small. C. The researcher should use the z-test because the population is assumed to be normally distributed. D. The t-test should be used because α and μ are unknown.
8. Because of the popularity of movies as an entertainment medium for adolescents, an entrepreneur plans to do a national study of the average cost of a movie ticket. If you assume that s = $0.50, what sample size would the entrepreneur have to take to be 95% confident that the estimate was within $0.25 of the true mean ticket prices?
A. 4 B. 16 C. 15 D. 8
9. If a teacher wants to test her belief that more than five students in college classes typically receive A as a grade, she'll perform _______-tail testing of a _______.
A. two, proportion B. one, mean C. two, mean D. one, proportion
10. To schedule appointments better, the office manager for an ophthalmologist wants to estimate the average time that the doctor spends with each patient. A random sample of 49 is taken, and the sample mean is 20.3 minutes. Assume that the office manager knows from past experience that the standard deviation is 14 minutes. She finds that a 95% confidence interval is between 18.3 and 22.3 minutes. What is the point estimate of the population mean, and what is the confidence coefficient?
A. 18.3, 95% B. 20.3, 95%
C. 18.3, 0.95 D. 20.3, 0.95
11. A human resources manager wants to determine a confidence interval estimate for the mean test score for the next office-skills test to be given to a group of job applicants. In the past, the test scores have been normally distributed with a mean of 74.2 and a standard deviation of 30.9. Determine a 95% confidence interval estimate if there are 30 applicants in the group.
A. 64.92 to 83.48 B. 13.64 to 134.76 C. 63.14 to 85.26 D. 68.72 to 79.68
12. In a simple random sample from a population of several hundred that's approximately normally distributed, the following data values were collected.
68, 79, 70, 98, 74, 79, 50, 102, 92, 96
Based on this information, the confidence level would be 90% that the population mean is somewhere between
A. 73.36 and 88.24. B. 65.33 and 95.33. C. 69.15 and 92.45. D. 71.36 and 90.24.
13. Determine the power for the following test of hypothesis. H0 :μ = 950 vs. H1 : μ =? 950, given that μ = 1,000, α = 0.10, σ = 200, and n = 25.
A. 0.6535 B. 0.5062 C. 0.3465 D. 0.4938
14. Consider a null hypothesis stating that the population mean is equal to 52, with the research hypothesis that the population mean is not equal to 52. Assume we have collected 38 sample data from which we computed a sample mean of 53.67 and a sample standard deviation of 3.84. Further assume the sample data appear approximately normal. What is the test statistic?
A. 2.68 B. -2.64 C. 2.64 D. -2.68
15. A portfolio manager was analyzing the price-earnings ratio for this year's performance. His boss said that the average price-earnings ratio was 20 for the many stocks that his firm had traded, but the portfolio manager felt that the figure was too high. He randomly selected a sample of 50 price-earnings ratios and found a mean of 18.17 and a standard deviation of 4.60. Assume that the population is normally distributed, and test at the 0.01 level of significance. Which of the following is the correct decision rule for the manager to use in this situation? A. Because 2.81 is greater than 2.33, reject H0. At the 0.01 level, the sample data suggest that the average price-earnings ratio for the stocks is less than 20. B. Because -2.81 falls in the rejection region, reject H0. At the 0.01 level, the sample data suggest that the average price- earnings ratio for the stocks is less than 20. C. If z > 2.33, reject H0.
D. If t > 2.68 or if t < -2.68, reject H0.
16. When the confidence coefficient is large, which of the following is true? A. The confidence interval is narrow. B. Its value is 1.0 or larger. C. Its value is close to 1.0, but not larger than 1.0.
D. It's more likely that the test will lead you to reject the null hypothesis. 17. The power of a test is the probability of making a/an _______ decision when the null hypothesis is
_______. A. correct, false B. incorrect, false C. correct, true D. incorrect, true
18. Which of the following statements about p-value testing is true? A. P-value testing applies only to one-tail tests. B. The p-value is the lowest significance level at which you should reject H0.
C. The p represents sample proportion. D. P-value testing uses a predetermined level of significance.
19. In sampling without replacement from a population of 900, it's found that the standard error of the mean, , is only two-thirds as large as it would have been if the population were infinite in size. What is the approximate sample size? A. 200 B. 400 C. 600 D. 500
20. The commissioner of the state police is reported as saying that about 10% of reported auto thefts involve owners whose cars haven't really been stolen. What null and alternative hypotheses would be appropriate in evaluating this statement made by the commissioner?
A. H0:p≥ 0.10 and H1:p < 0.10 B. H0:p = 0.10 and H1:p =? 0.10 C. H0:p ≤ 0.10 and H1:p > 0.10
D. H0:p> 0.10 and H1:p ≤ 0.10