1. A statistician buys a pack of 10 new golf balls, drops each golf ball from a height of one meter, and measures the height in centimeters it returns on the first bounce. The ten values are: 79.9 80.0 78.9 78.5 75.6 80.5 82.5 80.1 81.6 76.7 (a) Assume a normal N(75, 1) prior for . Find the posterior distribution of What is the Bayes estimate of Calculate a 95% Bayesian credible interval for Perform a Bayesian test of the hypothesis H0 : 80 vs H1 : < 80 (b) Assume a normal N(75, 102) prior for . Find the posterior distribution of What is the Bayes estimate of Calculate a 95% Bayesian credible interval for Perform a Bayesian test of the hypothesis H0 : 80 vs H1 : < 80 (c) Assume a normal N(75, 1002) prior for . Find the posterior distribution of What is the Bayes estimate of Calculate a 95% Bayesian credible interval for Perform a Bayesian test of the hypothesis H0 : 80 vs H1 : < 80 (d) Compare the results from 1a, 1b, and 1c. NOTE: NO CHATGPT IS REQUIRED. IF YOU USING CHATGPT..I WILL GIVE DISLIKE AND COMPLAINT TO CHEGG HELPLINE.