In a study by Erich Brandt of 70 restaurant bills, 40 of the 70 were paid using cash. We assume a random sample and esti

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In a study by Erich Brandt of 70 restaurant bills,40 of the 70 were paid using cash. We assume arandom sample and estimate the posterior distributionof the binomial parameter p, the populationproportion paying cash.a. Use a beta prior distribution with a = 2 andb = 2.b. Use a beta prior distribution with a = 1 andb = 1.c. Use a beta prior distribution with a and b verysmall and positive.d. Calculate a 95% credibility interval for p using(c). Is your interval compatible with p = .5?e. Calculate a 95% confidence interval for p usingEquation (8.10) of Section 8.2, and comparewith the result of (d).f. Calculate a 95% confidence interval for p usingEquation (8.11) of Section 8.2, and comparewith the results of (d) and (e).g. Compare the interpretations of the credibilityinterval and the confidence intervals.h. Based on the prior in (c), test the hypothesisp .5 using the posterior distribution tofindP( p .5).