Question

Given two independent random samples with the following results:

n1=233 pˆ1=0.63   

n2=435 pˆ2=0.76

Use this data to find the 95% confidence interval for the true difference between the population proportions.

Step 1 of 3: Find the critical value that should be used in constructing the confidence interval.

Step 2 of 3: Find the value of the standard error. Round your answer to three decimal places.

Step 3 of 3: Construct the 95% confidence interval. Round your answers to three decimal places.

Answer 1

Two-Proportion Confidence Interval

We need to construct the 95% confidence interval for the difference between population proportions p1​−p2. We have been provided with the following information: (a) Sample 1 - The sample size is N1 = 233, and the sample proportion is p^1​​=0.63 (b) Sample 2 - The sample size is N2 = 435, and the sample proportion is p^2​​=0.76 and the significance level is α=0.05 Critical Value Based on the information provided, the significance level is α=0.05, therefore the critical value is Zc​=1.96. This can be found by either using excel or the Z distribution table. Standard error: The confidence interval: Therefore, based on the data provided, the 95% confidence interval for the difference between the population proportions p1​−p2 is -0.2039<p1-p2<-0.0561, which indicates that we are 95% confident that the true difference between population proportions is contained by the interval