EXAMPLE 7.16 Planning a Survey of College Students
In Example 7.1 (page 361), we calculated a 95% confidence interval for the mean minutes per day a college student at your institution uses a smartphone. The margin of error based on an SRS of students was 21.2 minutes. Suppose that a new study is being planned and the goal is to have a margin of error of 15 minutes. How many students need to be sampled?
The sample standard deviation in Example 7.1 was 25.33. To be conservative, we’ll guess that the population standard deviation is 30 minutes.
400
To compute an initial , we replace with . This results in
Round up to get .
We now check to see if this sample size satisfies the requirement when we switch back to . For , we have degrees of freedom and . Using this value, the expected margin of error is
This is larger than , so the requirement is not satisfied.
The following table summarizes these calculations for some larger values of .
16 15.98 17 15.43 18 14.92 19 14.46
The requirement is first satisfied when . Thus, we need to sample at least students for the expected margin of error to be no more than 15 minutes.
Figure 7.12 shows the Minitab input window needed to do these calculations Because the default confidence level is 95%, only the desired margin of error and the estimate for need to be entered.
