Chapter 10, Problem 55SE

Young Criminals and Violence A statistics student performed a study on male and female criminals 15 years old and under who were on probation in Ventura County, California. The purpose was to see whether there was an association between type of crime (violent or nonviolent) and gender. Violent crimes involve physical contact such as hitting or fighting. Nonviolent crimes include vandalism, robbery, and verbal assault.

The raw data were shown in Exercise 10.3 on page 515. Use a two-sided alternative.

a. Make a two-way table that summarizes the data: use Boy and Girl across the top.

b. Compare the percentages of girls and boys who expressed violent behavior.

c. Test the hypothesis that gender and type of crime are associated, using the chi-square statistic. Use a significance level of 0.05.

d. Do a Fisher's Exact Test for the data with the same significance level. Report the two-tailed p-value and your conclusion. (Search for a Fisher's Exact Test calculator on the Internet.)

e. Compare the p-values from the chi-square test and Fisher's Exact Test. Which is more accurate?

f. Suppose the study had turned out differently. Create a new two-way summary table with the same row and column totals that yields a more extreme outcome in the direction you found. Report the p-value for this test, and compare it with the p-value you got in part d.