3 One-sided Binomial Confidence Intervals Scenario 1: We are analyzing 0-1 (binary or dummy) survey data with sample size n= 13. Define the random variable Xi = 1 if the person is satisfied, and zero if not where Xi Bernoulli(p) and cach is i.i.d. across all i = 1,2,..., 13 people surveyed. Let Y be the distribution (sum) of the n i.i.d. Bernoulli random variables. Accordingly, Y Binomial(n, p). 11. Suppose all 13 people surveyed were satisfied. Construct a 95% confidence interval for the unknown p without using the CLT. What is the smallest resonable value of p? Should our 95% confidence interval include p=0.83? (Note that you just need to use the CI bounds to find the answer). (7 pts) 12. Recall that from class we can verify the result to the above question by using the binomial probability of all successes out of n trials in the form Pr(Y = n) = p". Applying this logic, check your answer to question 11. (7 pts) 13. Consider now building a confidence interval for p, but under the assumption that all 13 people in our surveyed sample were NOT satisfied. Construct a 95% confidence interval for p without using the CLT. What is the largest reasonable value of p? Should our 95% confidence interval include p = 0.27? Use the CI bounds to determine the answer, and double check with the binomial probability of all failures out of n trials Pr(Y = 0) = (1 - p)". (7 pts)