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. (This data set was generated in Excel from a normal distribution with a mean of 529 and a std dev of 113.) 405 336 560 453 554 428 535 472 1. Based on this sample, find a point estimate of the population mean. 2. Use this sample to 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 99% 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 98% confidence? 6. How many students should be surveyed to estimate the mean score within 25 points with 90% confidence? 7. Compare your answers from questions 5 and 6. What effect does decreasing the confidence level have on the sample size required