Chapter 10: Problem 60
Suppose you randomly assign some parolees to check in once a week with their parole officers and others to check in once a month, and observe whether they are arrested within 6 months of starting parole.
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Chapter 10: Problem 60
Suppose you randomly assign some parolees to check in once a week with their parole officers and others to check in once a month, and observe whether they are arrested within 6 months of starting parole.
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Suppose you are interested in whether more than \(50 \%\) of voters in California support a proposition (Prop X). After the vote. you find the total number that support it and the total number that oppose it.
In a 2018 article published in The Lancet, Sprigg et al. studied the effect of tranexamic acid in treating patients with intracerebral hemorrhages using a randomized, placebo-controlled trial. Of the 1161 subjects treated with tranexamic acid, 383 suffered an adverse outcome after 2 days. Of the 1164 subjects given a placebo, 419 suffered an adverse outcome after 2 days. a. Find the percentage in each group that suffered an adverse outcome. Round off to one decimal place as needed. b. Create a two-way table with the treatment labels (drug/placebo) across the top. c. Test the hypothesis that treatment and adverse outcome are associated using a significance level of \(0.05\).
When playing Dreidel, (see photo) you sit in a circle with friends or relatives and take turns spinning a wobbly top (the dreidel). In the center of the circle is a pot of several foil-wrapped chocolate coins. If the four-sided top lands on the Hebrew letter gimmel, you take the whole pot and everyone needs to contribute to the pot again. If it lands on hey, you take half the pot. If it lands on \(n u n\), nothing happens. If it lands on shin, you put a coin in. Then the next player takes a turn. Each of the four outcomes is believed to be equally likely. One of the author's families got the following outcomes while playing with a wooden dreidel during Hanukah. Determine whether the outcomes allow us to conclude that the dreidel is biased (the four outcomes are not equally likely). Use a significance level of \(0.05 .\) $$\begin{array}{cccc}\text { gimmel } & \text { hey } & \text { nun } & \text { shin } \\\5 & 1 & 7 & 27\end{array}$$
Suppose there is a theory that \(90 \%\) of the people in the United States dream in color. You survey a random sample of 200 people; 198 report that they dream in color, and 2 report that they do not. You wish to verify the claim made in the theory.
In a 2009 study reported in the New England Journal of Medicine, Boyer et al. randomly assigned children aged 6 months to 18 years who had nonlethal scorpion stings to receive an experimental antivenom or a placebo. "Good" results were no symptoms after four hours and no detectable plasma venom. $$\begin{array}{|lccc|}\hline & \text { Antivenom } & \text { Placebo } & \text { Total } \\ \hline \text { No Improvement } & 1 & 6 & 7 \\ \hline \text { Improvement } & 7 & 1 & 8 \\\\\hline \text { Total } & 8 & 7 & 15 \\ \hline\end{array}$$ The alternative hypothesis is that the antivenom leads to improvement. The p-value for a one-tailed Fisher's Exact Test with these data is \(0.009\). a. Suppose the study had turned out differently, as in the following table. $$\begin{array}{|lcc|}\hline & \text { Antivenom } & \text { Placebo } \\ \hline \text { Bad } & 0 & 7 \\\\\hline \text { Good } & 8 & 0 \\ \hline\end{array}$$ Would Fisher's Exact Test have led to a p-value larger or smaller than \(0.009\) ? Explain. b. Suppose the study had turned out differently, as in the following table. $$\begin{array}{|lcc|}\hline & \text { Antivenom } & \text { Placebo } \\\\\hline \text { Bad } & 2 & 5 \\ \text { Good } & 6 & 2 \\\\\hline\end{array}$$ Would Fisher's Exact Test have led to a p-value larger or smaller than \(0.009\) ? Explain. c. Try the two tests, and report the p-values. Were you right? Search for a Fisher's Exact Test calculator on the Internet, and use it.
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