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Chapter 10: Problem 14
You flip a coin 100 times and get 58 heads and 42 tails. Calculate the chi- square statistic by hand, showing your work, assuming the coin is fair.
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The Perry Preschool Project data presented in exercise \(10.39\) (Schweinhart et al. 2005 ) can be divided to see whether the preschool attendance effect is different for males and females. The table shows a summary of the data for females, and the figure shows Minitab output that you may use. $$\begin{array}{|lcc|}\hline & \text { Preschool } & \text { No Preschool } \\\\\hline \text { HS Grad } & 21 & 8 \\\\\hline \text { HS Grad No } & 4 & 17 \\\ \hline\end{array}$$ a. Find the graduation rate for those females who went to preschool, and compare it with the graduation rate for females who did not go to preschool. b. Test the hypothesis that preschool and graduation rate are associated, using a significance level of \(0.05\).
Suppose a polling organization asks a random sample of people if they are Democrat, Republican, or Other and asks them if they think the country is headed in the right direction or the wrong direction. If we wanted to test whether party affiliation and answer to the question were associated, would this be a test of homogeneity or a test of independence? Explain.
In a 2015 study by Nanney et al. and published in the Journal of American College Health, a random sample of community college students was asked whether they ate breakfast 3 or more times weekly. The data are reported by gender in the table. $$\begin{array}{lcc}\text { Eat breakfast at least } 3 \times \text { weekly } & \text { Females } & \text { Males } \\\\\hline \text { Yes } & 206 & 94 \\\\\text { No } & 92 & 49 \\\\\hline\end{array}$$ a. Find the row, column, and grand totals, and prepare a table showing these values as well as the counts given. b. Find the percentage of students overall who eat breakfast at least three times weekly. Round off to one decimal place. c. Find the expected number who eat breakfast at least three times weekly for each gender. Round to two decimal places as needed. d. Find the expected number who did not eat breakfast at least three times weekly for each gender. Round to two decimal places as needed. e. Calculate the observed value of the chi-square statistic.
Refer to the description in exercise 10.71. There were 22 trials with only cockroaches (no robots) that went under one shelter. In 16 of these 22 trials, the group chose the darker shelter, and in 6 of the 22 the group chose the lighter shelter. There were 28 trials with a mixture of real cockroaches and robots that all went under one shelter. In 11 of these trials, the group chose the darker shelter, and in 17 the group chose the lighter shelter. The robot cockroaches were programmed to choose the lighter shelter (as well as preferring groups; Halloy et al. 2007 ) Is the introduction of robot cockroaches associated with the type of shelter when the group went under one shelter? Assume cockroaches were randomly sampled from some meaningful population of cockroaches. a. Use the chi-square test to see whether the presence or absence of robots is associated with whether they went under the darker or the brighter shelter. Use a significance level of \(0.05\) b. Do Fisher's Exact Test with the data. If your software does not do Fisher's Exact Test, search the Internet for a Fisher's Exact Test calculator and use it. Report the p-value and your conclusion. c. Compare the p-values for parts a and b. Which do you think is the more accurate procedure? The p-values that result from the two methods in this question are closer than the p-values in the previous question. Why do you think that is?
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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