When 16 seventeen-year-old women were randomly selected and tested with an aerobics test, the mean of their scores was found to be 37.9 with a sample standard deviation of 7.3. a) Construct both a 90% and a 99% confidence interval for the mean. Interpret the 99% interval. b) Explain why one interval is larger than the other c) How many people would need to be interviewed so that one could be 95% confident that the mean is in error by no more than 1.5 units? d) It is believed that this sample of seventeen-year-olds is not as aerobic as the national average of those participating in aerobics. The national average on this test is 40. Use appropriate hypothesis testing techniques to check the claim. (use = 0.05)