1. In lectures and in the labs, we discussed the Wald and Wilson methods for estimat-...

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1. In lectures and in the labs, we discussed the Wald and Wilson methods for estimat- ing the binomial parameter. Coverage probabilities are often used to determine the effectiveness of confidence intervals. For the binomial parameter 7 and fixed n, the coverage probability is n Ch(π) = Σπ(k, π) • Σ¹(K, π) (2) πª (1-x)" - k 2-k T k=0 where I(k, π) is an indicator of whether a confidence interval captures π if k successes are observed. (a) For a 95% confidence interval with n = 100 and π = 0.5, compute the coverage probabilities for both the Wald and Wilson confidence intervals. (b) Repeat part (a) for π = 0.05. (c) Compute coverage probabilities for n = 100 and possible values for 7 (with enough resolution) for 95% Wald and Wilson intervals and plot them using PROC SGPLOT. (d) Comment regarding the performance of both the Wald and Wilson intervals. 1. In lectures and in the labs, we discussed the Wald and Wilson methods for estimat- ing the binomial parameter. Coverage probabilities are often used to determine the effectiveness of confidence intervals. For the binomial parameter 7 and fixed n, the coverage probability is n Ch(π) = Σπ(k, π) • Σ¹(K, π) (2) πª (1-x)" - k 2-k T k=0 where I(k, π) is an indicator of whether a confidence interval captures π if k successes are observed. (a) For a 95% confidence interval with n = 100 and π = 0.5, compute the coverage probabilities for both the Wald and Wilson confidence intervals. (b) Repeat part (a) for π = 0.05. (c) Compute coverage probabilities for n = 100 and possible values for 7 (with enough resolution) for 95% Wald and Wilson intervals and plot them using PROC SGPLOT. (d) Comment regarding the performance of both the Wald and Wilson intervals.

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