# 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.