You have 36 observations from a distribution with an unknown mean µ. From your sample, you compute X¯ = 55 (sample mean) and s 2 = 49 (the sample variance). a. Write out a 95% confidence interval for µ. b. Write out a 99% confidence interval for µ. c. Compare your intervals from part a. and b. in terms of interval length. Why do they differ? d. Interest lies in if µ is greater than 50. Using your 95% confidence interval, in a sentence or two explain how you could answer if µ > 50.