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 had 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

Required:
a. Test the claim that the mean total score is 529 using either the classical approach (i. e., critical values and critical regions) or the P-value approach at the 0.05 level of significance.
b. Construct a 95% confidence interval (C. I.) for the true mean score for the population.
c. Does this interval contain the value reported by GMAC?
d. How many students should be surveyed to estimate the mean score within 25 points with 98% confidence?
e. How many students should be surveyed to estimate the mean score within 25 points with 90% confidence?
f. Compare your answers from questions 5 and 6. What effect does decreasing the confidence level have on the sample size required?