Assume X is distributed Chi-squared. You sample 61 observations from X and get a sample mean of 31 and sample variance of 62. a) At the 0.5% level of significance, conduct a hypothesis test to prove your belief that the population mean of X is greater than 29. b) Solve for the 1-sided 99.5% confidence interval given the direction of the alternative hypothesis as in part a) c) If you wanted to reduce the margin of error in part b) to be 1, assuming all else constant, then solve for the sample size required