#### Description:

In this video, we’ll show you how to calculate the sample size needed to achieve a confidence interval for One Proportion with a specified width and confidence level using PASS.

As an example, suppose we want to compute the sample size required for a two-sided 95% confidence interval if the sample proportion is 0.4 and the desired margin of error is plus or minus 3%.

To perform this calculation in PASS, first load the Confidence Intervals for One Proportion procedure using the category tree or the search bar on the PASS Home Window.

For Solve For, select Sample Size. This procedure also allows you to solve for interval width and confidence level.

This procedure allows you to compute sample sizes for both exact and approximate confidence intervals for one proportion. For this example, select Simple Asymptotic for the confidence interval formula.

Select Two-Sided for Interval Type for a two-sided confidence interval.

For a 95% confidence interval, we set Confidence Level to 0.95.

For a margin of error of plus or minus 3%, set the two-sided confidence interval width to 0.06.

Finally, set the sample proportion estimate to 0.4. Remember that the sample size calculations assume that the value entered here will be the actual proportion estimate that is obtained from the sample. If the sample proportion is different from the one specified here, the width may be narrower or wider than specified.

Now, click the Calculate button to perform the calculations and get the results. The required sample size for the desired interval is 1025.

For another example, suppose we want to calculate the sample size needed for an upper one-sided exact 95% confidence interval with an upper bound of 0.01 for a sample proportion of 0.

Go back to the procedure window and change the confidence interval formula to exact, Interval type to Upper One-Sided, the One-sided Distance to the Limit to 0.01, and the sample proportion to 0. If we run the calculation, the resulting sample size is 299.