LESSON 3: Sampling Distribution And Estimation; Hypothesis Testing
Questions 1–20: Select the one best answer to each question.
Use the following information to answer Questions 1–3.
In a simple random sample of 1000 households, 150 of these households happen to have sailboats. However, the characteristics of the population would make us expect the number of sailboat owners to be 180 in this sample.
1. What is the value of p?
2. What is the value of π?
3. What is the value of n?
4. In sampling without replacement from a population of 900, it’s found that the standard
error of the mean, σx, is only two-thirds as large as it would have been if the population were infinite in size. What is the approximate sample size?
5. If a teacher wants to test her belief that more than five students in college classes typically receive A as a grade, she will perform
A. two-tail testing of a mean.
B. one-tail testing of a mean.
C. two-tail testing of a proportion.
D. one-tail testing of a proportion.
6. 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: π = 0.10 and H1: π ≠ 0.10
B. H0: π ≤ 0.10 and H1: π > 0.10
C. H0: π ≥ 0.10 and H1: π < 0.10
D. H0: π > 0.10 and H1: π ≤ 0.10
7. In the statement of a null hypothesis, you would likely find which of the following terms?
8. To cut the maximum likely error (e) in half, the sample size (n) should be
A. decreased one-fourth.
B. decreased one-half.
C. increased by two times.
D. increased by four times.
9. A simple random sample with n = 700 is drawn from a binomial process in
which π = 0.7. With p = the proportion of successes, which of the following is the solution for P(0.65 ≤ p ≤ 0.70)?
10. 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?
11. For a given sample size, reducing the probability of a Type I error will
A. increase the probability of a Type II error.
B. decrease the probability of a Type II error.
C. have no effect on the probability of a Type II error.
D. seriously affect the standard deviation of the sample.
12. The last step in hypothesis testing is to
A. state the decision rule.
B. formulate the null and alternative hypotheses.
C. make the related business decision.
D. select the significance level.
13. 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.
14. Nondirectional assertions lead only to _______ tests.
15. If the population standard deviation isn’t known, what distribution should you use when testing a mean?
A. Standard normal
B. t distribution
16. 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?
17. In a simple random sample from a population 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. 71.36 and 90.24.
B. 69.15 and 92.45.
C. 65.33 and 95.33.
D. 73.36 and 88.24.
18. According to a 1997 study, 29.3% of self-employed persons worked on their home-based businesses 35 hours or more each week. What is the probability that at least 30.5% of 800 people randomly sampled from the study’s population worked on their businesses no less than 35 hours each week in 1997?
19. 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 σ is unknown and the sample size is small.
D. The researcher should use the z-test because the sample size is less than 30.
20. For 1996, the U.S. Department of Agriculture has 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 we can’t reject the claim that the average cottage cheese consumption in America is 2.6 pounds per person per year.
C. We can conclude that the average cottage cheese consumption in America is not 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.