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Chapter 7: Q3E (page 397)
What is the level of significance of a test of hypothesis?
The significance level is a predefined value of the probability of making a false decision.
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A border protection avatar. The National Center for Border Security and Protection has developed the "Embodied Avatar"—a kiosk with a computer-animated border guard that uses artificial intelligence to scan passports, check fingerprints, read eye pupils, and asks questions of travellers crossing the U.S. border. (National Defense Magazine, February 2014.) Based on field tests, the avatar's developer claims that the avatar can detect deceitful speech correctly 75% of the time.
a. Identify the parameter of interest.
b. Give the null and alternative hypotheses for testing the claim made by the avatar's developer.
c. Describe a Type I error in the words of the problem.
d. Describe a Type II error in the words of the problem
Refer to Exercise 7.99.
a. Find b for each of the following values of the population mean: 74, 72, 70, 68, and 66.
b. Plot each value of b you obtained in part a against its associated population mean. Show b on the vertical axis and m on the horizontal axis. Draw a curve through the five points on your graph.
c. Use your graph of part b to find the approximate probability that the hypothesis test will lead to a Type II error when m = 73.
d. Convert each of the b values you calculated in part a to the power of the test at the specified value of m. Plot the power on the vertical axis against m on the horizontal axis. Compare the graph of part b with the power curve of this part.
e. Examine the graphs of parts b and d. Explain what they reveal about the relationships among the distance between the true mean m and the null hypothesized mean m0, the value of b, and the power.
Performance of stock screeners. Recall, from Exercise 6.36 (p. 350), that stock screeners are automated tools used by investment companies to help clients select a portfolio of stocks to invest in. The data on the annualized percentage return on investment (as compared to the Standard & Poor’s 500 Index) for 13 randomly selected stock screeners provided by the American Association of Individual Investors (AAII) are repeated in the accompanying table. You want to determine whether \(\mu \) , the average annualized return for all AAII stock screeners, is positive (which implies that the stock screeners perform better, on average, than the S&P 500). An XLSTAT printout of the analysis is shown on the top of page 418.
9.0 -.1 -1.6 14.6 16.0 7.7 19.9 9.8 3.2 24.8 17.6 10.7 9.1
Latex allergy in health care workers (cont’d). Refer to Exercise 7.120. Let \({\sigma ^2}\) represent the variance in the number of latex gloves used per week by all hospital employees. Consider testing \({H_0}:{\sigma ^2} = 100\) against\({H_a}:{\sigma ^2} \ne 100.\)
a. Give the rejection region for the test at a significance level of\(\alpha = 0.01.\)
b. Calculate the value of the test statistic.
c. Use the results, parts a and b, to make the appropriate conclusion.
A two-tailed test was conducted with the null and alternative hypotheses stated being \({H_0}:p = .69\) against \({H_a}:p \ne .69\), respectively, with a sample size of 150. The test results were z = -.98 and two-tailed p-value = .327
a. Determine the conditions required for a valid large sample test
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