is the best point estimate for , therefore, the best point estimate of the population mean is with
Now, for 95% confidence interval,
To find the area under the normal curve = .4750, the corresponding z value for this area is 1.96.
55.352 < 62.397
Solution
Therefore, to be 90% confident that the estimate is within $150 of the true mean monthly salary, the researcher needs a sample size of at least 147 sports reporters.