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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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Accidents at construction sites. In a study published in the Business & Economics Research Journal (April 2015), occupational accidents at three construction sites in Turkey were monitored. The total numbers of accidents at the three randomly selected sites were 51, 104, and 37.
Summary statistics for these three sites are:\(\bar x = 64\)and s = 35.3. Suppose an occupational safety inspector claims that the average number of occupational accidents at all Turkish construction sites is less than 70
a. Set up the null and alternative hypotheses for the test.
b. Find the rejection region for the test using\(\alpha = .01\)
c. Compute the test statistic.
d. Give the appropriate conclusion for the test.
e. What conditions are required for the test results to be valid?
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.
If you select a very small value for when conducting a hypothesis test, will tend to be big or small? Explain.
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.
Ages of cable TV shoppers. Cable TV鈥檚 Home Shopping Network (HSN) reports that the average age of its shoppers is 52 years. Suppose you want to test the null hypothesis,\({H_0}:\mu = 52\), using a sample of\(n = 50\) cable TV shoppers.
a. Find the p-value of a two-tailed test if\(\overline x = 53.3\)and\(s = 7.1\)
b. Find the p-value of an upper-tailed test if\(\overline x = 53.3\)and\(s = 7.1\)
c. Find the p-value of a two-tailed test if\(\overline x = 53.3\)and\(s = 10.4\)
d. For each of the tests, parts a鈥揷, give a value of\(\alpha \)that will lead to a rejection of the null hypothesis.
e. If\(\overline x = 53.3\), give a value of s that will yield a two-tailed p-value of 0.01 or less.
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