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Chapter 7: Q27E (page 403)
An analyst tested the null hypothesis that μ ≥ 20against the alternative hypothesis that μ <20. The analyst reported a p-value of .06. What is the smallest value ofαfor which the null hypothesis would be rejected?
Therefore, the smallest value of the significance level is α = 0.06.
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Americans’ favorite sport. The Harris Poll (December 2013) conducted an online survey of American adults to determine their favorite sport. Your friend believes professional (National Football League [NFL]) football—with revenue of about $13 billion per year—is the favorite sport for 40% of American adults. Specify the null and alternative hypotheses for testing this belief. Be sure to identify the parameter of interest.
A t-test is conducted for the null hypothesis versus the alternative for a random sample of n = 17 observations. The test results are t = 1.174, p-value = 0.1288.
a. Interpret the p-value.
For the binomial sample sizes and null hypothesized values of p in each part, determine whether the sample size is large enough to use the normal approximation methodology presented in this section to conduct a test of the null hypothesis \({H_0}:p = {p_0}\)
Revenue for a full-service funeral. According to the National Funeral Directors Association (NFDA), the nation's 19,000 funeral homes collected an average of \(7,180 per full-service funeral in 2014 (www.nfda.org). A random sample of 36 funeral homes reported revenue data for the current year. Among other measures, each reported its average fee for a full-service funeral. These data (in thousands of dollars) are shown in the following table.
a. What are the appropriate null and alternative hypotheses to test whether the average full-service fee of U. S. funeral homes this year is less than \)7,180?
b. Conduct the test at\(\alpha = 0.05\). Do the sample data provide sufficient evidence to conclude that the average fee this year is lower than in 2014?
c. In conducting the test, was it necessary to assume that the population of average full-service fees was normally distributed? Justify your answer
a. List three factors that will increase the power of a test.
b. What is the relationship between b, the probability of committing a Type II error, and the power of a test?
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