In a study by Erich Brandt of 70 restaurant bills,
40 of the 70 were paid using cash. We assume a
random sample and estimate the posterior distribution
of the binomial parameter p, the population
proportion paying cash.
a. Use a beta prior distribution with a = 2 and
b = 2.
b. Use a beta prior distribution with a = 1 and
b = 1.
c. Use a beta prior distribution with a and b very
small 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 using
Equation (8.10) of Section 8.2, and compare
with the result of (d).
f. Calculate a 95% confidence interval for p using
Equation (8.11) of Section 8.2, and compare
with the results of (d) and (e).
g. Compare the interpretations of the credibility
interval and the confidence intervals.
h. Based on the prior in (c), test the hypothesis
p .5 using the posterior distribution to
find
P( p .5).