Chapter 4: Problem 85
State the conclusion of the test based on this p-value in terms of "Reject \(H_{0} "\) or "Do not reject \(H_{0} "\), if we use a \(5 \%\) significance level. p-value \(=0.0320\)
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Match the four \(\mathrm{p}\) -values with the appropriate conclusion: (a) The evidence against the null hypothesis is significant, but only at the \(10 \%\) level. (b) The evidence against the null and in favor of the alternative is very strong. (c) There is not enough evidence to reject the null hypothesis, even at the \(10 \%\) level. (d) The result is significant at a \(5 \%\) level but not at a \(1 \%\) level. I. 0.00008 II. 0.0571 III. 0.0368 IV. \(\quad 0.1753\)
For each situation described, indicate whether it makes more sense to use a relatively large significance level (such as \(\alpha=0.10\) ) or a relatively small significance level (such as \(\alpha=0.01\) ). Testing to see whether taking a vitamin supplement each day has significant health benefits. There are no (known) harmful side effects of the supplement.
The same sample statistic is used to test a hypothesis, using different sample sizes. In each case, use StatKey or other technology to find the p-value and indicate whether the results are significant at a \(5 \%\) level. Which sample size provides the strongest evidence for the alternative hypothesis? Testing \(H_{0}: p=0.5\) vs \(H_{a}: p>0.5\) using \(\hat{p}=0.55\) with each of the following sample sizes: (a) \(\hat{p}=55 / 100=0.55\) (b) \(\hat{p}=275 / 500=0.55\) (c) \(\hat{p}=550 / 1000=0.55\)
A confidence interval for a sample is given, followed by several hypotheses to test using that sample. In each case, use the confidence interval to give a conclusion of the test (if possible) and also state the significance level you are using. A \(99 \%\) confidence interval for \(\mu: 134\) to 161 (a) \(H_{0}: \mu=100\) vs \(H_{a}: \mu \neq 100\) (b) \(H_{0}: \mu=150 \mathrm{vs} H_{a}: \mu \neq 150\) (c) \(H_{0}: \mu=200\) vs \(H_{a}: \mu \neq 200\)
Scientists studying lion attacks on humans in Tanzania \(^{32}\) found that 95 lion attacks happened between \(6 \mathrm{pm}\) and \(10 \mathrm{pm}\) within either five days before a full moon or five days after a full moon. Of these, 71 happened during the five days after the full moon while the other 24 happened during the five days before the full moon. Does this sample of lion attacks provide evidence that attacks are more likely after a full moon? In other words, is there evidence that attacks are not equally split between the two five-day periods? Use StatKey or other technology to find the p-value, and be sure to show all details of the test. (Note that this is a test for a single proportion since the data come from one sample.)
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