In Montreal, Canada, an experiment was done with parents of children who were thought to have a high risk of committing crimes when they became teenagers. Some of the families were randomly assigned to receive parental training, and the others were not. Out of 43 children whose parents were randomly assigned to the parental training group, 6 had been arrested by the age of 15. Out of 123 children whose parents were not in the parental training group, 37 had been arrested by age 15.
a. Find and compare the percentages of children arrested by age 15. Is this what researchers might have hoped?
b. Create a two-way table from the data, and test whether the treatment program is associated with arrests. Use a significance level of 0.05.
c. Do a two-proportion z-test, testing whether the parental training lowers the rate of bad results. Use a significance level of 0.05.
d. Explain the difference in the results of the chi-square test and the two-proportion z-test.
e. Can you conclude that the treatment causes the better result? Why or why not?