15.11
Body mass index of young women. Example 14.1 (page 360) assumed that the body mass index (BMI) of all American young women follows a Normal distribution with standard deviation How large a sample would be needed to estimate the mean BMI in this population to within with 95% confidence?
Solution
This is direct from the formula
where is the number of samples, is the standard deviation of the Normal distribution, is the margin of error, and is the critical value for the corresponding confidence.
In our case, the problem gives us , , and we compute the critical value from table C: for a confidence of 95%. Application of the formula gives then Remember to round always up; therefore the answer must be: we need a sample of at least 217 young women to estimate a mean BMI within with 95% confidence.
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