Question

Assume that a sample is used to estimate a population proportion p. Find the 99% confidence interval for a sample of size 297 with 166 successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places. 99% C.I. = Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

Answer 1

One-Proportion Confidence Interval

We need to construct the 99% confidence interval for the population proportion. We have been provided with the following information: The sample size is N = 297, the number of favorable cases is X = 166 and the sample proportion is pˉ​=X/N​=166/297​=0.5589, and the significance level is α=0.01 Critical Value Based on the information provided, the significance level is α=0.01, therefore the critical value is Zc​=2.5758. This can be found by either using excel or the Z distribution table. Margin of Error The confidence interval: Therefore, based on the data provided, the 99% confidence interval for the population proportion is 0.4847<p<0.6331, which indicates that we are 99% confident that the true population proportion p is contained by the interval