EXAMPLE 6.4

Average college savings fund contribution. One survey question asked how much money from a college savings fund, such as a 529 plan, is used to pay for college. Of the 1600 who were surveyed, n = 1593 provided an answer. Nonresponse should always be considered as a source of bias. In this case, the nonresponse is very low, so we’ll proceed by treating the n = 1593 sample as if it were an unbiased sample.

The average amount is $1768. It’s very likely that this distribution is highly skewed to the right with many small amounts and a few very large amounts. 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 amount contributed from a college savings fund among all undergraduates. We’ll assume that the standard deviation for the population of college savings fund contributions is $1483. For 95% confidence, we see from Table D that z* = 1.960. The margin of error for the 95% confidence interval for μ 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 will do the same for the margin of error. Keeping additional digits would provide no additional useful information. Therefore, we will use m = 37. The approximate 95% confidence interval is

= (1731, 1805)

We are 95% confident that the mean amount contributed from a college savings fund among all undergraduates is between $1731 and $1805.