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. -3.32
B. 0.95
C. 3.32
D. 6.69
2. Nondirectional assertions lead only to _______ tests.
A. one-tail
B. right-tail
C. two-tail
D. left-tail
3. Determine which of the following four population size and sample size combinations would not require the use of the finite population correction factor in calculating the standard error.
A. N = 150; n = 25
B. N = 15,000; n = 1,000
C. N = 2500; n = 75
D. N = 1500; n = 300
4. 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. 8
D. 15
5. 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 p-value you would report for this test?
A. 0.4963
B. 0.0037
C. 0.0041
D. 0.4959
6. 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
7. 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. 68.72 to 79.68
B. 63.14 to 85.26
C. 13.64 to 134.76
D. 64.92 to 83.48
8. In the statement of a null hypothesis, you would likely find which of the following terms?
A. =
B. >
C. <
D. ≠
9. 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 population is assumed to be normally distributed.
B. The researcher should use the z-test because the sample size is less than 30.
C. The t-test should be used because α and μ are unknown.
D. The t-test should be used because the sample size is small.
10. H0 is p = 0.45 and H1 is p ≠ 0.45. What type of test will be performed?
A. One-tail testing of a mean
B. Two-tail testing of a mean
C. One-tail testing of a proportion
D. Two-tail testing of a proportion
11. 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, 0.95
B. 20.3, 95%
C. 20.3, 0.95
D. 18.3, 95%
12. For 1996, the U.S. Department of Agriculture estimated that American consumers would have eaten, on average, 2.6 pounds of cottage cheese throughout the course of that year. Based on a longitudinal study of 98 randomly selected people conducted during 1996, the National Center for Cottage Cheese Studies found an average cottage cheese consumption of 2.75 pounds and a standard deviation of s = 14 ounces. Given this information, which of the following statements would be correct concerning a two-tail test at the 0.05 level of significance?
A. We can conclude that the average cottage cheese consumption in America is actually 2.75 pounds per person per year.
B. We can conclude that we can't reject the claim that the average cottage cheese consumption in America is 2.6 pounds per
person per year.
C. We can conclude that the average cottage cheese consumption in America isn't 2.6 pounds per person per year.
D. We can conclude that the average cottage cheese consumption in America is at least 0.705 pound more or less than 2.75
pounds per person per year.
13. What sample size is required from a very large population to estimate a population proportion within 0.05 with 95% confidence? Don't assume any particular value for p.
A. 271
B. 385
C. 767
D. 38
14. Which of the following statements correctly compares the t-statistic to the z-score when creating a confidence interval?
A. Using t is easier because you do not have to worry about the degrees of freedom, as you do with z.
B. The value of z relates to a normal distribution, while the value of t relates to a Poisson distribution.
C. Use t when the sample size is small, and the resulting confidence interval will be narrower.
D. You can use t all the time, but for n ≥ 30 there is no need, because the results are almost identical if you use t or z.
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 falls in the rejection region, reject H0. At the 0.01 level, the sample data suggest that the average priceearnings ratio for the stocks is less than 20.
B. 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.
C. If z > 2.33, reject H0.
D. If t > 2.68 or if t < -2.68, reject H0.
16. A mortgage broker is offering home mortgages at a rate of 9.5%, but the broker is fearful that this value is higher than many others are charging. A sample of 40 mortgages filed in the county courthouse shows an average of 9.25% with a standard deviation of 8.61%. Does this sample indicate a smaller average? Use α = 0.05 and assume a normally distributed population.
A. No, because the test statistic falls in the acceptance region.
B. Yes, because the test statistic is greater than -1.645.
C. Yes, because the sample mean of 9.25 is below 9.5.
D. No, because the test statistic is -1.85 and falls in the rejection region.
17. The Coca-Cola Company has 40% of the cola market. Determine the probability that a sample proportion for n = 30 is within 0.10 of the true population proportion of 0.40, which represents the proportion of cola drinkers who prefer a Coca-Cola drink.
A. 0.9198
B. 0.4599
C. 0.7372
D. 0.3686
18. 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. 71.36 and 90.24.
C. 69.15 and 92.45.
D. 65.33 and 95.33.
19. 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 p-value you would report for this test?
A. 0.0041
B. 0.0074
C. 0.4963
D. 0.0037
20. If the level of significance (α) is 0.005 in a two-tail test, how large is the nonrejection region under the End of exam curve of the t distribution?
A. 0.9975
B. 0.005
C. 0.995
D. 0.050