# Exam: sampling distributions and estimation; hypothesis testing

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. 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. 63.14 to 85.26
C. 68.72 to 79.68
D. 13.64 to 134.76

2. 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. 0.0037
B. 0.4963
C. 0.0074
D. 0.0041

3. 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 α and μ are 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.

4. Which of the following statements about p-value testing is true?
A. The p represents sample proportion.
B. P-value testing uses a predetermined level of significance.
C. The p-value is the lowest significance level at which you should reject H0
D. P-value testing applies only to one-tail tests.

5. In a criminal trial, a Type II error is made when a/an
A. innocent person is acquitted.
B. guilty defendant is convicted.
C. guilty defendant is acquitted.
D. innocent person is convicted.

6. What is the rejection region for a two-tailed test when α = 0.05?
A. |z | > 1.645
B. |z | > 1.96
C. |z | > 2.575
D. z > 2.575

7. 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. –2.68
C. –2.64
D. 2.64

8. 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.

9. 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. 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.

10. 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. 16B. 4
C. 8
D. 15

11. 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. 500
B. 600
C. 400
D. 200

12. 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 = 150; n = 25
C. N = 15,000; n = 1,000
D. N = 1500; n = 300

13. 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 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 at least 0.705 pound more or less than 2.75 pounds per person per year.

14. 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

15. 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, mean
B. one, proportionEnd of exam
C. two, proportion
D. one, mean

16. 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. 0.005
C. 0.995
D. 0.050

17. 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. If you don’t apply the correction coefficient, your confidence intervals will be too narrow, and thus overconfident.
C. When the sample is a very small portion of the population, the correction coefficient is required.
D. If you don’t apply the correction coefficient, your confidence intervals will be too broad, and thus less useful in decision making.

18. Nondirectional assertions lead only to _______-tail tests.
A. two
B. left
C. one
D. right

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. 18.3, 95%
B. 20.3, 0.95
C. 20.3, 95%
D. 18.3, 0.95

20. 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. In both the one-tailed and two-tailed tests, the rejection region is one contiguous interval on the number line.
C. The test will never confirm the null hypothesis, only fail to reject the null hypothesis.
D. A Type I error is the chance that the researcher rejects the null hypothesis when in fact the null hypothesis is true.

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