Returning to the previous exercise, the mean and standard deviation of the number of credit cards for the no-involvement group were 2.22 and 1.58, respectively, whereas the mean and standard deviation for the payment-help group were 2.09 and 1.65, respectively. Does it appear that the true average number of cards for noinvolvement students exceeds the average for payment-help students? Carry out an appropriate test of significance.

Data From Exercise 21

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Credit card spending and resulting debt pose very real threats to consumers in general, and the potential for abuse is especially serious among college students. It has been estimated that about two-thirds of all college students possess credit cards, and 80% of these students received cards during their first year of college. The article "College Students' Credit Card Debt and the Role of Parental Involvement: Impli- cations for Public Policy" (J. Public Policy Mark. 2001: 105-113) reported that for 209 students whose parents had no involvement whatsoever in credit card acquisition or payments, the sample mean total account balance was $421 with a sample standard deviation of $686, whereas for 75 students whose parents assisted with payments even though they were under no legal obligation to do so, the sample mean and sample standard deviation were $666 and $1048, respectively. All sampled students were at most 21 years of age. a. Do you think it is plausible that the distributions of total debt for these two types of students are normal? Why or why not? Is it necessary to assume normality in order to compare the two groups using an inferential procedure described in this chapter? Explain. b. Estimate the true average difference between total balance for noninvolve- ment students and postacquisition- involvement students using a method that incorporates precision into the estimate. Then interpret the estimate.