7-1 Estimating a Population Proportion 323 Clopper-Pearson Method The Clopper-Pearson method is an “exact” method in the sense that it is based on the exact binomial distribution instead of an approximation of a distribution. Disadvantage of the Clopper-Pearson Confidence Interval Too “Conservative”: The coverage probability is usually greater than or equal to the selected confidence level. Calculations with the Clopper-Pearson method are too messy to consider here. Which Method Is Best? There are other methods for constructing confidence intervals that are not discussed here. There isn’t universal agreement on which method is best for constructing a confidence interval estimate of p. ■ The Wald confidence interval is best as a teaching tool for introducing students to confidence intervals. ■ The plus four confidence interval is almost as easy as Wald and it performs better than Wald by having a coverage probability closer to the selected confidence level. Again, note that except for some Beyond the Basic exercises, the exercises that follow are based on the Wald confidence interval given earlier, not the better-performing confidence intervals discussed here. TECH CENTER Proportions: Confidence Intervals and Sample Size Determination Access tech supplements, videos, and data sets at www.TriolaStats.com Confidence Interval 1. Click Stat in the top menu. 2. Select Basic Statistics from the dropdown menu and select 1 Proportion from the submenu. 3. Select Summarized data in the dropdown window and enter the number of events (successes) and number of trials. Confirm Perform hypothesis test is not checked. 4. Click the Options button and enter the desired confidence level. For Alternative Hypothesis select 3 and for Method select Normal approximation for the methods of this section. 5. Click OK twice. Sample Size Determination Minitab determines sample size using the binomial distribution (not normal distribution), so the results will differ from those found using the methods of this section. 1. Click Stat in the top menu. 2. Select Power and Sample Size from the dropdown menu and select Sample Size for Estimation from the submenu. 3. For Parameter select Proportion (Binomial) and enter an estimate of the proportion if known or enter 0.5 if not known. 4. Select Estimate sample sizes from the dropdown menu and enter the margin of error for confidence intervals. 5. Click the Options button to enter the confidence level and select a two-sided confidence interval. 6. Click OK twice. Minitab Confidence Interval 1. Click Analysis in the top menu. 2. Select Confidence Intervals from the dropdown menu and select Proportion One Sample from the submenu. 3. Enter the confidence level, sample size, and number of successes. 4. Click Evaluate. Sample Size Determination 1. Click Analysis in the top menu. 2. Select Sample Size Determination from the dropdown menu and select Estimate Proportion from the submenu. 3. Enter the confidence level, margin of error E, estimate of p if known, and population size if known. 4. Click Evaluate. Statdisk continued
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