Question

A recent survey asked parents of school-aged children about their children's access to technology at home. In a sample of 915 rural families, 23% said they did not have access to a computer at home. In a sample of 2386 suburban families, 13% said they did not have access to a computer at home. In this problem, you'll perform a two-sample hypothesis test of proportions at the 1% significance level, testing whether the difference in the percentage of families without computer access between rural and suburban populations (Rural - Urban) is greater than zero.

Calculate the Test Statistic

Find the Critical Value

Answer 1

let us consider the null and alternative hypothesis is

Ho:p1 =p2

Ha:p1 > p2

using excel>Addin>phstat>two sample test

we have

Z Test for Differences in Two Proportions
Data
Hypothesized Difference	0
Level of Significance	0.01
Group 1
Number of Items of Interest	211
Sample Size	915
Group 2
Number of Items of Interest	310.18
Sample Size	2386
Intermediate Calculations
Group 1 Proportion	0.23
Group 2 Proportion	0.13
Difference in Two Proportions	0.1
Average Proportion	0.18
Z Test Statistic	6.693909335
Upper-Tail Test
Upper Critical Value	2.326347874
p-Value	1.08643E-11
Reject the null hypothesis

the Test Statistic is 6.694

the Critical Value is 2.3264