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Chapter 7: Q27E (page 403)
An analyst tested the null hypothesis that 渭 鈮� 20against the alternative hypothesis that 渭 <20. The analyst reported a p-value of .06. What is the smallest value of伪for which the null hypothesis would be rejected?
Therefore, the smallest value of the significance level is 伪 = 0.06.
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鈥淪treaming鈥� of television programs is trending upward. According to The Harris Poll (August 26, 2013), over one-third of American鈥檚 qualify as 鈥渟ubscription streamers,鈥� i.e., those who watch streamed TV programs through a subscription service such as Netflix, Hulu Plus, or Amazon Prime. The poll included 2,242 adult TV viewers, of which 785 are subscription streamers. On the basis of this result, can you conclude that the true fraction of adult TV viewers who are subscription streamers differs from one-third? Carry out the test using a Type I error rate of . Be sure to give the null and alternative hypotheses tested, test statistic value, rejection region or p-value, and 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.
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.
Refer to Exercise 6.44 (p. 356), in which 50 consumers taste-tested a new snack food. Their responses (where 0 = do not like; 1 = like; 2 = indifferent) are reproduced below
Americans鈥� 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鈥攚ith revenue of about $13 billion per year鈥攊s 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.
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