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Suppose you observe Y1,...,Yn, where each Yi is 0 (no) or 1 (yes). Assume that Y1,...,Yn...

Suppose you observe Y1,...,Yn, where each Yi is 0 (no) or 1 (yes). Assume that Y1,...,Yn are independent and identically distributed. Define p = E[Yi], which is unknown.

  1. What is the standard deviation of the sample average? Use p in this answer.

  2. Note that the maximum value for p is 1 and the minimum is 0. What is the largest standard deviation of the sample average? (Maximize the previous answer over p.) What is the sample size n which makes the standard deviation of the sample average less than 5%?

  3. What is the standard error of the sample average? (You cannot use p in this question.)

  4. What is the 95% confidence interval?

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