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Questions 1 to 20: 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. Which of the following statements correctly compares the t-statistic to the z-score when creating a
confidence interval?
A. 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.
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. Using t is easier because you do not have to worry about the degrees of freedom, as you do with z.
2. Nondirectional assertions lead only to _______-tail tests.
A. one
B. right
C. two
D. left
3. 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. If t > 2.68 or if t < –2.68, reject H0.
B. 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.
C. If z > 2.33, reject H0.
D. 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.
4. What is the rejection region for a two-tailed test when α = 0.05?
A. z > 2.575
B. |z | > 1.96
C. |z | > 1.645
D. |z | > 2.575
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 test statistic?
A. –2.64
B. 2.68
C. 2.64
D. –2.68
6. When the confidence coefficient is large, which of the following is true?
A. Its value is 1.0 or larger.
B. Its value is close to 1.0, but not larger than 1.0.
C. The confidence interval is narrow.
D. It's more likely that the test will lead you to reject the null hypothesis.
7. 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. 0.9975
B. 0.995
C. 0.005
D. 0.050
8. What is the primary reason for applying a finite population correction coefficient?
A. When the sample is a very small portion of the population, the correction coefficient is required.
B. If you don't apply the correction coefficient, your confidence intervals will be too broad, and thus less useful in decision making.
C. If you don't apply the correction coefficient, you won't have values to plug in for all the variables in the confidence interval formula.
D. If you don't apply the correction coefficient, your confidence intervals will be too narrow, and thus overconfident.
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. one, proportion
B. two, mean
C. two, proportion
D. one, mean
10. 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. 0.0037
C. 0.4963
D. 0.0074
11. 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. 3
B. 4
C. 30
D. 2.5
12. 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. 400
B. 500
C. 200
D. 600
13. The power of a test is the probability of making a/an _______ decision when the null hypothesis is
_______.
A. correct, false
B. incorrect, true
C. correct, true
D. incorrect, false
14. 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. 15
C. 16
D. 8
15. 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. 20.3, 0.95
B. 18.3, 0.95
C. 18.3, 95%
D. 20.3, 95%
16. 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. 385
B. 271
C. 767
D. 38
17. 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 at least 0.705 pound more or less than 2.75
pounds per person per year.
B. We can conclude that the average cottage cheese consumption in America isn't 2.6 pounds per person per year.
C. 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.
D. We can conclude that the average cottage cheese consumption in America is actually 2.75 pounds per person per year.
18. 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. –3.32
C. 3.32
D. 6.69
19. 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 = 2500; n = 75
B. N = 1500; n = 300
C. N = 15,000; n = 1,000
D. N = 150; n = 25
20. 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 t-test should be used because the sample size is small.
C. The researcher should use the z-test because the sample size is less than 30.
D. The t-test should be used because α and μ are unknown.
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