EXAMPLE 6.7

How many undergraduates should we survey? Suppose that we are planning a survey similar to the one described in Example 6.4 (page 350). If we want the margin of error for the average amount contributed from a college savings plan to be $30 with 95% confidence, what sample size n do we need? For 95% confidence, Table D gives z* = 1.960. For σ we will use the value from the previous study, $1483. If the margin of error is $30, we have

Because 9387 measurements will give a slightly wider interval than desired and 9388 measurements a slightly narrower interval, we should choose n = 9388. We need information from 9388 undergraduates to determine an estimate of mean college savings fund contribution with the desired margin of error.