Example 11

EXAMPLE 11 Sample size for estimating the population mean

We round up because (a) the sample size must be a whole number and (b) rounding down will lead to a value of with less than the desired confidence level.

Suppose we want to estimate to within $1000 the mean salary of all college graduates who were business majors. Assume . How many business majors would we sample to estimate the mean salary to within $1000 with 95% confidence?

Solution

“Within $1000” means that the desired margin of error is $1000, and 1.96 is the value associated with 95% confidence. Substituting into the formula for the sample size, we get:

Now, when finding the required sample size, if the formula results in a decimal, we always round up to the next whole number. Thus, we need a sample size of for a confidence level of 95%.

NOW YOU CAN DO

Exercises 47–54.