Work out the following problems. Show your work. 1. Your instructor has 8 chickens (all of which are hens), and is curious about how many eggs they laid per week, compared to other (independent) youps of chickens. They collected data from 20 independent coops with 8 hens, and found the following for the number of eggs laid per week: 10, 20,21, 21,21, 22, 24, 25,26, 28,31, 33, 34, 35,36, 36,36, 38, 40, 48 The claim is that the median for number of eggs laid is less than 37 (what your instructor measured in their coop). (a) (3 points] State the null and alternative, and calculate the approriate test-statistic for using the exact binomial test. (13) (4 points) Calcualte the p-value and interpret it in terms of the problem. If you cannot remember how to calculate the p-value, you may still interpret the same. (c) (4 points) Find the 95% condence interval for the CDF of the dataset at the value 35, using the normal approxi- mation to binomial. (d) (3 points) What is the highest percentile that the value 35 is likely to be? Explain your