Bayesian probability interval

Suppose Rebekah's prior beliefs about the proportion P are represented by a beta curve with parameters 8.13 and 7.67.

After observing results from a survey, Rebekah's posterior distribution are represented by a beta curve with parameters 24.13 and 7.67. Rebekah's 90% probability interval for P is given by (0.627, 0.872).

Compare this Bayesian interval with a 90% classical interval, and pick out the false statement below!

Possible Answers

Since Rebekah is using prior information, the width of the Bayesian interval will be shorter than the classical interval.
The Bayesian and classical intervals will have approximately the same length.
The probability P is contained in the Bayesian interval is exactly 0.90.
The Bayesian interval using Rebekah's prior will be shorter than the Bayesian interval using a uniform prior.

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Bayesian probability interval

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