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 random sample of 100 observations from a population with standard deviation 60 yields a sample mean of 110. Test the null hypothesis that H μ = 100 versus Hα μ > 100 using α = .05

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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 random sample of 100 observations from a population with standard deviation 60 yields a sample mean of 110. Test the null hypothesis that H : μ = 100 versus Hα : μ > 100 using α = .05

A. z = 1.96

B. z = 1.67

C. z = 1.69

D. z = 2.09

2. A company that develops artificial intelligence designed to detect false statements has developed a program that police officers can use to determine whether a criminal suspect is lying or not. According to the company, the AI can detect false statements correctly 75% of the time. What are the null and alternative hypothesis for testing the claim that the AI detects false statements as claimed by the company? A. H0 : p = .25, Hα : p ≠ .25

B. H0 : p = .75, Hα : p ≠ .75

C. H0 : p = .01, Hα : p ≠ .01

D. H0 : p = .99, Hα : p ≠ .99

3. Determine the power for the following test of hypothesis. H0 : μ = 950 vs. H1 : μ ≠ 950, given than μ = 1,000, α = 0.10, σ = 200, and n = 25.

A. 0.3465

B. 0.4938

C. 0.5062

D. 0.6535

4. 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’s the point estimate of the population mean, and what’s the confidence coefficient? A. 20.3, 0.95

B. 18.3, 0.95

C. 18.3, 0.05

D. 20.3, 0.05

5. A random sample of 70 observations from a normally distributed population produced a mean of x = 26.2 and a standard deviation of s = 4.1. Find an approximate 99% confidence interval for the population mean, μ. A. 25.1 ± .169

B. 26.2 ± .1.26

C. 26.4 ± .156

D. 28.3 ± .155

6. Consider a null hypothesis stating that the population mean is equal to 52, with the research hypothesis that the population mean isn’t equal to 52. Assume you’ve 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’s the p-value you would report for this test? A. 0.0025

B. 0.0074

C. 0.0084

D. 0.0041

7. 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. 13.64 to 134.76

D. 63.14 to 85.26

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? A. 3

B. 30

C. 4

D. 2.5

9. Assuming N = 10,000, n = 4,000, and s = 50, compute the standard error of x using the finite population correction factor. A. .6024

B. .6124

C. .5931

D. .6358

10. Using a sample size of n = 400. If σ = 20 and x = 72.5, find the value of the test statistic. Consider the test H0 : μ = 70 versus Hα : μ > 70

A. 2.5

B. 2.3

C. 1.8

D. 2.25

11. What’s 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

12. Construct a 90% confidence interval for p for a random sample of size n = 121 yielded A. 8.8 ± .698

B. 9.2 ± .182

C. 8.9 ± .145

D. 8.8 ± .049

13. Assume a random sample of n = 5 measurements from a normal distribution. Compare the standard normal z-values with the corresponding t-values if you were forming a 99% confidence interval. A. 1.96; 2.776

B. 1.645; 2.132

C. 1.282; 1.533

D. 2.576; 4.604

14. Where is the rejection region if t > 1.440 and df = 6? A. α = .02 B. α = .10 C. α = .05 D. α = .01

15. In the statement of a null hypothesis, you would likely find which of the following terms? A. =

B. <

C. >

D. +

16. Nondirectional assertions lead only to _______-tail tests. A. right

End of exam

B. left

C. one

D. two

17. Your state decides to mandate a shortened 30-hour workweek for all companies with 20 or more employees. Economics researchers studying the impacts of a shortened work week on unemployment rates found several key variables, including whether employees held multiple jobs, hourly wages, and level of employment across the economy. Assuming that the year before the enactment of the 30-hour workweek law unemployment in your state was 12%. In a random sample of 500 employable residents of the state, 53 were unemployed. Conduct a test of hypothesis to determine if your state’s unemployment rate dropped after the shortened workweek law was passed. Test using α = 0.05 A. z = –.96

B. z = –.90

C. z = .96

D. z = –.88

18. What type of test will be performed? H is p = 0.45 and H1 is p ≠ 0.45

A. One-tail testing of a mean

B. One-tail testing of a proportion

C. Two-tail testing of a proportion

D. Two-tail testing of a mean

19. Which element of a test of a hypothesis is used to decide whether to reject the null hypothesis in favor of the alternative hypothesis? A. Rejection region

B. Test statistic

C. Level of significance

D. Conclusion

20. 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. Yes, because the sample mean of 9.25 is below 9.5.

B. No, because the test statistic falls in the acceptance region.

C. No, because the test statistic is –1.85 and falls in the rejection region.

D. Yes, because the test statistic is greater than –1.645.

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