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Chapter 7: Q20E (page 403)
If a hypothesis test were conducted using 伪= 0.05, for which of the following p-values would the null hypothesis be rejected?
a. .06
b. .10
c. .01
d. .001
e. .251
f. .042
The null hypothesis would be rejected for every case because all of the given p-values are less than the 伪 value.
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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.
Suppose the sample in Exercise 7.64 has produced \(\hat p = .83\) and we wish to test \({H_0}:P = 0.9\) against the alternative \({H_a}:p < .9\)
a. Calculate the value of the z-statistic for this test.
Latex allergy in health care workers (cont鈥檇). 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 random sample of 64 observations produced the following summary statistics: \(\bar x = 0.323\) and \({s^2} = 0.034\).
a. Test the null hypothesis that\(\mu = 0.36\)against the alternative hypothesis that\(\mu < 0.36\)using\(\alpha = 0.10\).
b. Test the null hypothesis that \(\mu = 0.36\) against the alternative hypothesis that \(\mu \ne 0.36\) using \(\alpha = 0.10\). Interpret the result.
We reject the null hypothesis when the test statistic falls in the rejection region, but we do not accept the null hypothesis when the test statistic does not fall in the rejection region. Why?
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