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, 414, 570, 521, 663, 727, 413
1. Find a point estimate of the population mean.
2. Construct a 95% confidence interval (C.I.) for the true mean score for the population.
3. Does this interval contain the value reported by GMAC?
4. Now use this same sample to construct a 98% C.I. What is it? How does it compare to the 95% C.I.?
5. How many students should be surveyed to estimate the mean score within 25 points with 90% confidence?
6. How many students should be surveyed to estimate the mean score within 25 points with 95% confidence?
7. Compare your answers from questions 5 and 6. What effect does increasing the confidence level have on the sample size required?