# statistics business economics sampling distribution and estimation

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

2. 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. 600
B. 400
C. 200
D. 500

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

4. 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. 0.0041
C. 0.0037
D. 0.0074

5. 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. 15
B. 16
C. 8
D. 4

6. What is the purpose of sampling?
A. To verify that the population is approximately normally distributed
B. To estimate a target parameter of the population
C. To create a point estimator of the population mean or proportion
D. To achieve a more accurate result than can be achieved by surveying the entire population

7. 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, 95%
B. 18.3, 95%
C. 18.3, 0.95
D. 20.3, 0.95

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

9. 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. 13.64 to 134.76
C. 63.14 to 85.26
D. 64.92 to 83.48

10. 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 t-test should be used because the sample size is small.
B. The researcher should use the z-test because the sample size is less than 30.
C. The researcher should use the z-test because the population is assumed to be normally distributed.
D. The t-test should be used because α and μ are unknown.

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

12. 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. 65.33 and 95.33.
B. 71.36 and 90.24.
C. 69.15 and 92.45.
D. 73.36 and 88.24.

13. 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. 0.995
B. 0.050
C. 0.005
D. 0.9975

14. 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 we can’t reject the claim that the average cottage cheese consumption in America is 2.6 pounds per person per year.
B. We can conclude that the average cottage cheese consumption in America is actually 2.75 pounds per person per year.
C. 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.
D. We can conclude that the average cottage cheese consumption in America isn’t 2.6 pounds per person per year.

15. 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
End of exam
B. 2.64
C. –2.64
D. 2.68

16. H0  is p = 0.45 and H1 is p ≠ 0.45. What type of test will be performed?
A. Two-tail testing of a proportion
B. One-tail testing of a proportion
C. Two-tail testing of a mean
D. One-tail testing of a mean

17. 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

18. 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. H 0: p ≥ 0.10 and H 1: p < 0.10

B. H 0 : p = 0.10 and H 1 : p ≠ 0.10

C. H 0: p ≤ 0.10 and H1: p > 0.10
D. H 0 : p > 0.10 and H1: p ≤ 0.10

19. 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. 2.5
B. 4
C. 30
D. 3

20. 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. Using t is easier because you do not have to worry about the degrees of freedom, as you do with z.
C. Use t when the sample size is small, and the resulting confidence interval will be narrower.
D. The value of z relates to a normal distribution, while the value of t relates to a Poisson distribution. 