# Sampling distributions and estimation; hypothesis testing

Sampling Distributions and Estimation; Hypothesis TestingWhen you have completed your exam and reviewed your answers, click Submit Exam. Answers will not be recorded until youhit Submit Exam. If you need to exit before completing the exam, click Cancel Exam.Questions 1 to 20: Select the best answer to each question. Note that a question and its answers may be split across a pagebreak, so be sure that you have seen the entire question and all the answers before choosing an answer.1. A random sample of 10 employees is selected from a large firm. For the 10 employees, the number ofdays each was absent during the past month was found to be 0, 2, 4, 2, 5, 1, 7, 3, 2, and 4. Of thefollowing values, which would you use as the point estimate for the average number of days absent for allthe firm’s employees?A. 3B. 2.5C. 30D. 42. In a criminal trial, a Type II error is made when a/anA. guilty defendant is acquitted.B. innocent person is convicted.C. guilty defendant is convicted.D. innocent person is acquitted.3. What is the purpose of sampling?A. To create a point estimator of the population mean or proportionB. To achieve a more accurate result than can be achieved by surveying the entire populationC. To verify that the population is approximately normally distributedD. To estimate a target parameter of the population4. What is the rejection region for a two-tailed test when α = 0.05?A. |z | > 1.96B. z > 2.575C. |z | > 2.575D. |z | > 1.6455. Which of the following statements about p-value testing is true?A. P-value testing uses a predetermined level of significance.B. P-value testing applies only to one-tail tests.C. The p represents sample proportion.D. The p-value is the lowest significance level at which you should reject H0.6. Which of the following statements correctly compares the t-statistic to the z-score when creating aconfidence 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. Using t is easier because you do not have to worry about the degrees of freedom, as you do with z.D. Use t when the sample size is small, and the resulting confidence interval will be narrower.7. If a teacher wants to test her belief that more than five students in college classes typically receive A as agrade, she’ll perform _______-tail testing of a _______.A. two, meanB. two, proportionC. one, meanD. one, proportion8. Which of the following statements about hypothesis testing is false?A. The rejection region is always given in units of standard deviations from the mean.B. A Type I error is the chance that the researcher rejects the null hypothesis when in fact the null hypothesis is true.C. In both the one-tailed and two-tailed tests, the rejection region is one contiguous interval on the number line.D. The test will never confirm the null hypothesis, only fail to reject the null hypothesis.9. Consider a null hypothesis stating that the population mean is equal to 52, with the research hypothesisthat the population mean is not equal to 52. Assume we have collected 38 sample data from which wecomputed a sample mean of 53.67 and a sample standard deviation of 3.84. Further assume the sampledata appear approximately normal. What is the test statistic?A. 2.64B. 2.68C. –2.64D. –2.6810. A mortgage broker is offering home mortgages at a rate of 9.5%, but the broker is fearful that this valueis higher than many others are charging. A sample of 40 mortgages filed in the county courthouse shows anaverage 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. Yes, because the test statistic is greater than –1.645.B. No, because the test statistic is –1.85 and falls in the rejection region.C. No, because the test statistic falls in the acceptance region.D. Yes, because the sample mean of 9.25 is below 9.5.11. A researcher wants to carry out a hypothesis test involving the mean for a sample of n = 20. While thetrue value of the population standard deviation is unknown, the researcher is reasonably sure that thepopulation is normally distributed. Given this information, which of the following statements would becorrect?A. The t-test should be used because the sample size is small.B. The t-test should be used because α and μ are unknown.C. The researcher should use the z-test because the sample size is less than 30.D. The researcher should use the z-test because the population is assumed to be normally distributed.12. The power of a test is the probability of making a/an _______ decision when the null hypothesis is_______.A. correct, trueB. incorrect, trueC. correct, falseD. incorrect, false13. Determine which of the following four population size and sample size combinations would not requirethe use of the finite population correction factor in calculating the standard error.A. N = 150; n = 25B. N = 1500; n = 300C. N = 15,000; n = 1,000D. N = 2500; n = 7514. When the confidence coefficient is large, which of the following is true?A. Its value is 1.0 or larger.B. It’s more likely that the test will lead you to reject the null hypothesis.C. The confidence interval is narrow.D. Its value is close to 1.0, but not larger than 1.0.15. In sampling without replacement from a population of 900, it’s found that the standard error of themean, , is only two-thirds as large as it would have been if the population were infinite in size. What isthe approximate sample size?A. 500B. 600C. 400D. 20016. What sample size is required from a very large population to estimate a population proportion within0.05 with 95% confidence? Don’t assume any particular value for p.A. 385B. 38C. 271D. 76717. H0 is p = 0.45 and H1 is p ≠ 0.45. What type of test will be performed?A. Two-tail testing of a proportionB. Two-tail testing of a meanC. One-tail testing of a meanEnd of examD. One-tail testing of a proportion18. A portfolio manager was analyzing the price-earnings ratio for this year’s performance. His boss saidthat the average price-earnings ratio was 20 for the many stocks that his firm had traded, but the portfoliomanager felt that the figure was too high. He randomly selected a sample of 50 price-earnings ratios andfound a mean of 18.17 and a standard deviation of 4.60. Assume that the population is normallydistributed, and test at the 0.01 level of significance. Which of the following is the correct decision rule forthe 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 priceearningsratio 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 ratiofor the stocks is less than 20.19. Nondirectional assertions lead only to _______-tail tests.A. rightB. oneC. leftD. two20. A woman and her son are debating about the average length of a preacher’s sermons on Sundaymorning. 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 astandard deviation of 6.69 minutes. Assuming that the population is normally distributed and using a 0.05level of significance, he wishes to determine whether he is correct in thinking that the average length ofsermons is more than 20 minutes. What is the test statistic?A. 0.95B. 6.69C. 3.32D. –3.32