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Chapter 7: Q25 E (page 403)
In a test of \({H_0}:\mu = 100\) against \({H_a}:\mu \ne 100\), the sample data yielded the test statistic z = 2.17. Find the p-value for the test.
The p-value for the hypothesis test is 0.030.
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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鈥攖he point-spread error鈥攚as 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 伪 = 0.10.
Question:Paying for music downloads. If you use the Internet, have you ever paid to access or download music? This was one of the questions of interest in a Pew Internet & American Life Project Survey (October 2010). In a representative sample of 755 adults who use the Internet, 506 admitted
that they have paid to download music. Let p represent the true proportion of all Internet-using adults who have paid to download music.
a. Compute a point estimate of p.
b. Set up the null and alternative hypotheses for testing whether the true proportion of all Internet-using adults who have paid to download music exceeds.7.
c. Compute the test statistic for part b.
d. Find the rejection region for the test if 伪 = 0.01.
e. Find the p-value for the test.
f. Make the appropriate conclusion using the rejection region.
g. Make the appropriate conclusion using the p-value.
For each of the following rejection regions, sketch the sampling distribution for z and indicate the location of the rejection region.
a. \({H_0}:\mu \le {\mu _0}\) and \({H_a}:\mu > {\mu _0};\alpha = 0.1\)
b. \({H_0}:\mu \le {\mu _0}\) and \({H_a}:\mu > {\mu _0};\alpha = 0.05\)
c. \({H_0}:\mu \ge {\mu _0}\) and \({H_a}:\mu < {\mu _0};\alpha = 0.01\)
d. \({H_0}:\mu = {\mu _0}\) and \({H_a}:\mu \ne {\mu _0};\alpha = 0.05\)
e. \({H_0}:\mu = {\mu _0}\) and \({H_a}:\mu \ne {\mu _0};\alpha = 0.1\)
f. \({H_0}:\mu = {\mu _0}\) and \({H_a}:\mu \ne {\mu _0};\alpha = 0.01\)
g. For each rejection region specified in parts a鈥揻, state the probability notation in z and its respective Type I error value.
Arresting shoplifters. Shoplifting in the United States costs retailers about $35 million a day. Despite the seriousness of the problem, the National Association of shoplifting Prevention (NASP) claims that only 50% of all shoplifters are turned over to police (www.shopliftingprevention.org). A random sample of 40 U.S. retailers were questioned concerning the disposition of the most recent shoplifter they apprehended. A total of 24 were turned over to police. Do these data provide sufficient evidence to contradict the NASP?
a. Conduct a hypothesis test to answer the question of interest. Use\(\alpha = 0.05\).
b. Is the sample size large enough to use the inferential procedure of part a?
c. Find the observed significance level of the hypothesis test in part a. Interpret the value.
d. For what values \(\alpha \) would the observed significance level be sufficient to reject the null hypothesis of the test you conducted in part b?
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.
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