Question: The Non-Profit Times conducted a random sample of 126 U.S. non-profit companies at the beginning of 2005. The results reported that the average salary of an executive director of a nonprofit was $92,411 per year with a sample standard deviation of $25,326. A research team from a competing newspaper, which was skeptical of these results, conducted a survey of its own with the same size sample of companies and obtained a mean salary of $87,566 for executive directors (with approximately the same standard deviation as the Non-Profit Times’s sample).

a) Set up the appropriate null and alternative hypotheses for testing whether the original sample overestimated the average executive director annual salary.

b) Now test the competing newspaper’s view that the original sample overestimated the average executive director annual salary. Use an estimation (total) error of 5 percent.