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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Question: Point spreads of NFL games. Refer to the Chance (Fall 1998) study of point-spread errors in NFL games, Exercise 7.41 (p. 411). Recall that the difference between the actual game outcome and the point spread established by odds makers—the point-spread error—was calculated for 240 NFL games. The results are summarized as follows: . Suppose the researcher wants to know whether the true standard deviation of the point spread errors exceeds 15. Conduct the analysis using α = 0.10.
Accuracy of price scanners at Walmart. Refer to Exercise 6.129 (p. 377) and the study of the accuracy of checkout scanners at Walmart stores in California. Recall that the National Institute for Standards and Technology (NIST) mandates that for every 100 items scanned through the electronic checkout scanner at a retail store, no more than two should have an inaccurate price. A study of random items purchased at California Walmart stores found that 8.3% had the wrong price (Tampa Tribune, Nov. 22, 2005). Assume that the study included 1,000 randomly selected items.
a. Identify the population parameter of interest in the study.
b. Set up H0 and Ha for a test to determine if the true proportion of items scanned at California Walmart stores exceeds the 2% NIST standard.
c. Find the test statistic and rejection region (at ) for the test.
d. Give a practical interpretation of the test.
e. What conditions are required for the inference, part d, to be valid? Are these conditions met?
Producer's and consumer's risk. In quality-control applications of hypothesis testing, the null and alternative hypotheses are frequently specified as\({H_0}\)The production process is performing satisfactorily. \({H_a}\): The process is performing in an unsatisfactory manner. Accordingly, \(\alpha \) is sometimes referred to as the producer's risk, while \(\beta \)is called the consumer's risk (Stevenson, Operations Management, 2014). An injection molder produces plastic golf tees. The process is designed to produce tees with a mean weight of .250 ounce. To investigate whether the injection molder is operating satisfactorily 40 tees were randomly sampled from the last hour's production. Their weights (in ounces) are listed in the following table.
a. Write \({H_0}\) and \({H_a}\) in terms of the true mean weight of the golf tees, \(\mu \).
b. Access the data and find \(\overline x \)and s.
c. Calculate the test statistic.
d. Find the p-value for the test.
e. Locate the rejection region for the test using\({H_a} = 0.01\).
f. Do the data provide sufficient evidence to conclude that the process is not operating satisfactorily?
g. In the context of this problem, explain why it makes sense to call \(\alpha \)the producer's risk and \(\beta \)the consumer's risk.
Specify the differences between a large-sample and a small-sample test of a hypothesis about a population mean m. Focus on the assumptions and test statistics.
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
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