Question

Question 2. (10 marks) A manager is interested in estimating a population proportion. A sample of size n = 100 yields 42 successes. Based on these sample data, compute a 99% confidence interval estimate for the true population proportion.

Answer 1

99% confident that the true population proportion p is contained by the interval (0.293,0.547).

We need to construct the 99% confidence interval for the population proportion. We have been provided with the following information about the number of favorable cases: Favorable Cases X = 42 Sample Size N = 100 100 and the number The sample proportion is computed as follows, based on the sample size N of favorable cases X = 42: P X N 42 100 0.42 The critical value for a = 0.01 is ze = 21-a/2 = 2.576. The corresponding confidence interval is computed as shown below: CI(Proportion) p(1-7) p(1-P) p - Zc1 P + zc1 n n 0.42 - 2.576 x 0.42(1 – 0.42) 100 0.42 +2.576 x 0.42(1 – 0.42) 100 (0.293, 0.547) Therefore, based on the data provided, the 99% confidence interval for the population proportion is 0.293 <p<0.547, which indicates that we are 99% confident that the true population proportion pis contained by the interval (0.293, 0.547).