EXAMPLE 6.10 Average Credit Card Balance among College Students
Starting in 2008, Sallie Mae, a major provider of education loans and savings programs, has conducted an annual study titled “How America Pays for College.” Unlike other studies on college funding, this study assesses all aspects of spending and borrowing, for both educational and noneducational purposes. In the 2012 survey, 1601 randomly selected individuals (817 parents of undergraduate students and 784 undergraduate students) were surveyed by telephone.8
Many of the survey questions focused on the undergraduate student, so the parents in the survey were responding for their children. Do you think we should combine responses across these two groups? Do you think your parents are fully aware of your spending and borrowing habits? The authors reported overall averages and percents in their report but did break things down by group in their data tables. For now, we consider this a sample from one population, but we revisit this issue later.
One survey question asked about the undergraduate’s current total outstanding balance on credit cards. Of the 1601 who were surveyed, only provided an answer. Nonresponse should always be considered as a source of bias. In this case, the authors believed this nonresponse to be an ignorable source of bias and proceeded by treating the sample as if it were a random sample. We will do the same.
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The average credit card balance was $755. The median balance was $196, so this distribution is clearly skewed. Nevertheless, because the sample size is quite large, we can rely on the central limit theorem to assure us that the confidence interval based on the Normal distribution will be a good approximation.
Let’s compute an approximate 95% confidence interval for the true mean credit card balance among all undergraduates. We assume that the standard deviation for the population of credit card debts is $1130. For 95% confidence, we see from Table D that . The margin of error for the 95% confidence interval for is, therefore,
We have computed the margin of error with more digits than we really need. Our mean is rounded to the nearest $1, so we do the same for the margin of error. Keeping additional digits would provide no additional useful information. Therefore, we use . The approximate 95% confidence interval is
We are 95% confident that the average credit card debt among all undergraduates is between $659 and $851.