5. The standard deviation of train accidents in a month in England is o=15.1 (assumed to be known). Assume the number of train accidents in a month is independent of the number in any other month. The mean number of train accidents per month is /. a. Suppose one intends to collect a random sample of monthly train accident totals over the last 20 years. One wishes to test the null hypothesis , : / = 100 versus the two-sided alternative that # # 100 . One wishes to sample enough months / to have 80% power to detect a difference =110 at the 0.05 significance level. How many monthly records are required? (5 points) b. If n = 24 months are sampled at random, and a 90% confidence interval is constructed from the data, how wide will the confidence interval be? (5 points) c. Consider the confidence interval width calculated in part b. Call that width W. How many samples are required to reduce that width 2/3rds? That is, how many are required so that the resulting confidence interval has width w/3? (5 points)