Chapter 8: Problem 58
When, in a criminal court, a defendant is found "not guilty," is the court saying with certainty that he or she is innocent? Explain.
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Chapter 8: Problem 58
When, in a criminal court, a defendant is found "not guilty," is the court saying with certainty that he or she is innocent? Explain.
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Shift workers, who work during the night and must sleep during the day, often become sleepy when working and have trouble sleeping during the day. In a study done at Harvard Medical School, 209 shift workers were randomly divided into two groups; one group received a new sleep medicine (modafinil, or Provigil), and the other group received a placebo. During the study, \(54 \%\) of the workers taking the placebo and \(29 \%\) of those taking the medicine reported accidents or near accidents commuting to and from work. Assume that 104 of the people were assigned the medicine and 105 were assigned the placebo. (Source: Czeisler et al., Modafinil for excessive sleepiness associated with shift-work sleep disorder, New England Joumal of Medicine, vol. 353: \(476-486\), August 4,2005 ) a. State the null and altemative hypothesis. Is the alternative hypothesis one-sided or two-sided? Explain your choice. b. Perform a statistical test to determine whether the difference in proportions is significant at the \(0.05\) level.
A professor creates two versions of a 20 -question multiple-choice quiz. Each question has four choices. One student got a score of 19 out of 20 for the version of the test given to the person sitting next to her. The professor thinks the student was copying another exam. The student admits that he hadn't studied for the test, but he says he was simply guessing on each question and just got lucky. For the professor, the null hypothesis is that \(p=0.25\), where \(p\) is the probability that the student chooses the correct answer if just guessing, and the alternative is \(p>0.25\). Would you say that the p-value for this hypothesis test will be high or low? Explain.
Mercury in Freshwater Fish (Example 11) Some experts believe that \(20 \%\) of all freshwater fish in the United States have such high levels of mercury that they are dangerous to eat. Suppose a fish market has 250 fish tested, and 60 of them have dangerous levels of mercury. Test the hypothesis that this sample is not from a population with \(20 \%\) dangerous fish. Use a significance level of \(0.05\). Comment on your conclusion: Are you saying that the percentage of dangerous fish is definitely \(20 \%\) ? Explain.
A proponent of a new proposition on a ballot wants to know whether the proposition is likely to pass. Suppose a poll is taken, and 580 out of 1000 randomly selected people support the proposition. Should the proponent use a hypothesis test or a confidence interval to answer this question? Explain. If it is a hypothesis test, state the hypotheses and find the test statistic, p-value, and conclusion. If a confidence interval is appropriate, find the approximate \(95 \%\) confidence interval. In both cases, assume that the necessary conditions have been met.
Choose one of the answers given. The null hypothesis is always a statement about a (sample statistic or population parameter).
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