Exam 050273RR – SAMPLING DISTRIBUTIONS AND ESTIMATION HYPOTHESIS TESTING_Answer
Exam 050273RR – SAMPLING DISTRIBUTIONS AND ESTIMATION HYPOTHESIS TESTING_Answer
1. 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. 64.92 to 83.48
C. 63.14 to 85.26
D. 13.64 to 134.76
2. 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 average of $54.98 for this sample
D. The auditor should survey the total of all accounts and determine the mean.
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 = 2500; n = 75B.N = 15,000; n = 1,000C.N = 1500; n = 300D.N = 150; n = 254. 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.
5.H0 is p = 0.45 and H1 is p ≠ 0.45. What type of test will be performed?
A. One-tail testing of a proportion
B. Two-tail testing of a proportion
C. One-tail testing of a mean
D. Two-tail testing of a mean
6. Which of the following statements about p-value testing is true?
A.P-value testing applies only to one-tail tests.
B. The p represents sample proportion.
C. The p-value is the lowest significance level at which you should reject H0.
D.P-value testing uses a predetermined level of significance.
7. What is the primary reason for applying a finite population correction coefficient?
A. 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.
B. When the sample is a very small portion of the population, the correction coefficient is required.
C. If you don’t apply the correction coefficient, your confidence intervals will be too broad, and thus less useful in decision making.
D. If you don’t apply the correction coefficient, your confidence intervals will be too narrow, and thus overconfident.
8. 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?
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 t-test should be used because αand μare unknown.
C. The t-test should be used because the sample size is small.
D. The researcher should use the z-test because the sample size is less than 30.
10. 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, 96Based on this information, the confidence level would be 90% that the population mean is somewhere between
A. 73.36 and 88.24.
B. 69.15 and 92.45.
C. 65.33 and 95.33.
D. 71.36 and 90.24.
11. What is the rejection region for a two-tailed test when α= 0.05?
A. |z | > 1.645
B.z > 2.575
C. |z | > 2.575
D. |z | > 1.96
12. 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?
13. 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
A. one-tail testing of a proportion.
B. two-tail testing of a proportion.
C. two-tail testing of a mean.
D. one-tail testing of a mean.
14. 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?
15. 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
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. No, because the test statistic is –1.85 and falls in the rejection region.
C. Yes, because the test statistic is greater than –1.645.
D. Yes, because the sample mean of 9.25 is below 9.5.
17. In the statement of a null hypothesis, you would likely find which of the following terms?
D. < 18. Which of the following statements about hypothesis testing is false? A. In both the one-tailed and two-tailed tests, the rejection region is one contiguous interval on the number line. B. The test will never confirm the null hypothesis, only fail to reject the null hypothesis. C. A Type I error is the chance that the researcher rejects the null hypothesis when in fact the null hypothesis is true. D. The rejection region is always given in units of standard deviations from the mean. 19. 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, 95% C. 20.3, 95% D. 18.3, 0.95 20. 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. If z > 2.33, reject H0.
C. 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.
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.
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