problem-8.27

problem-8.27  We have n1 = n2 = 10,000 and \phat1=.216, \phat2=.193. A two-sided significance test is performed with prop.test() as follows:
> n = c(10000,10000)
> phat = c(.216,.193)
> x = n*phat
> prop.test(x,n,conf.level = 0.01)

        2-sample test for equality of proportions with
        continuity correction

data:  x out of n
X-squared = 16.12, df = 1, p-value = 5.952e-05
alternative hypothesis: two.sided
1 percent confidence interval:
 0.02283 0.02317
sample estimates:
prop 1 prop 2
 0.216  0.193
    
The difference is statistically significant. However, if the surveys were only of size 1,000m the difference would not have been statistically significant.