In a study of 70 restaurant bills, 40 of the 70 were paid using cash. Let p
Question:
In a study of 70 restaurant bills, 40 of the 70 were paid using cash. Let p denote the population proportion paying cash.
a. Assuming a beta prior distribution for p with α0 = 2 and β0 = 2, obtain the posterior distribution of p.
b. Repeat (a) with a0 and b0 positive and close to 0.
c. Calculate a 95% credible interval for p using (b). Is your interval compatible with p = .5?
d. Calculate a 95% confidence interval for p using Equation (5.3), and compare with the result of (c).
Equation 5.3
e. Compare the interpretations of the credible interval and the confidence interval.
f. Based on the prior in (b), test the hypothesis p ≤ .5 by using the posterior distribution to find P(p ≤ .5).
Step by Step Answer:
Modern Mathematical Statistics With Applications
ISBN: 9783030551551
3rd Edition
Authors: Jay L. Devore, Kenneth N. Berk, Matthew A. Carlton