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Chapter 7: Q114S (page 387)
A random sample of 175 measurements possessed a mean and a standard deviation s = .79.
a. Test against Use
猞� The Z-statistic does not fall into the rejection region. So, we fail to reject the
null hypothesis.
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A border protection avatar. The National Center for Border Security and Protection has developed the "Embodied Avatar"鈥攁 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
A simple random sample of 25 observations was selected from a normal population. The mean and standard deviation of this sample are 20 and 5, respectively.
a. Test against at the 10% significance level.
b. Test against at the 1% significance level.
EPA limits on vinyl chloride. The EPA sets an airborne limit of 5 parts per million (ppm) on vinyl chloride, a colorless gas used to make plastics, adhesives, and other chemicals. It is both a carcinogen and a mutagen (New Jersey Department of Health, Hazardous Substance Fact Sheet, 2010). A major plastics manufacturer, attempting to control the amount of vinyl chloride its workers are exposed to, has given instructions to halt production if the mean amount of vinyl chloride in the air exceeds 3.0 ppm. A random sample of 50 air specimens produced the following statistics: \(\overline x = 3.1\)ppm,\(s = 0.5\)ppm.
a. Do these statistics provide sufficient evidence to halt the production process? Use\(\alpha = 0.01\).
b. If you were the plant manager, would you want to use a large or a small value for\(\alpha \)the test in part a? Explain.
c. Find the p-value for the test and interpret its value
In a test of against, the sample data yielded the test statistic z = 2.17. Find and interpret the p-value for the test.
Shopping vehicle and judgment. Refer to the Journal of Marketing Research (December 2011) study of grocery store shoppers鈥� judgments, Exercise 2.85 (p. 112). For one part of the study, 11 consumers were told to put their arm in a flex position (similar to carrying a shopping basket) and then each consumer was offered several choices between a vice product and a virtue product (e.g., a movie ticket vs. a shopping coupon, pay later with a larger amount vs. pay now). Based on these choices, a vice choice score was determined on a scale of 0 to 100 (where higher scores indicate a greater preference for vice options). The data in the next table are (simulated) choice scores for the 11 consumers. Suppose that the average choice score for consumers with an extended arm position (similar to pushing a shopping cart) is known to be \(\mu = 50\) . The researchers theorize that the mean choice score for consumers shopping with a flexed arm will be higher than 43 (reflecting their higher propensity to select a vice product) Test the theory at \(\alpha = 0.05\)
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