The Graduate Management Admission Test (GMAT) is a test required for admission into many masters of business administration (MBA) programs. Total scores on the GMAT are normally distributed and historically have a population standard deviation of 113. The Graduate Management Admission Council (GMAC), who administers the test, claims that the mean total score is 529.

Suppose a random sample of 8 students took the test, and their scores are given below.

699

560

514

570

521

663

727

513

How many students should be surveyed to estimate the mean score within 25 points with 98% confidence?

How many students should be surveyed to estimate the mean score within 25 points with 90% confidence?

Compare your answers from questions 5 and 6. What effect does decreasing the confidence level have on the sample size required?