For an upcoming congressional election, suppose we want to estimate the amount of support for a particular

Question:

For an upcoming congressional election, suppose we want to estimate the amount of support for a particular candidate in a district. By previous experience and voter registration data, we can assume that the prior of the proportion of support, p, is a beta with μ = 10, and β = 8 (i.e. π(p) ~ Beta (10, 8)). We conducted a survey of 1000 randomly selected voters, of whom 600 support the candidate. Obtain a 95% credible interval for p. What will happen to the credible interval if we reduce the confidence interval? What will happen to the 95% credible interval if we increase the sample size? Distribution
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