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).

Transcribed Image Text:

E(5XY² − 4XY + e* + 12) = 5E(XY²) — 4E(XY) + E(ex) + 12