Question

This problem is from the "Using R for Introductory Statistics" by John Verzani. Problem 9.22:

In the year 2001, a poll of 600 people found that 250 supported gay marriage. A 2013 poll of 1,050 found 52% in support. Do a test of significance to see whether the difference in proportions is statistically significant.

Answer 1

Solution:

Here, we have to use two sample z test for population proportions.

H₀: p1 = p2 versus H_a: p1 ≠ p2

(two tailed test)

We are given

n1 = 600,

n2 = 1050

x1 = 250,

x2 = 1050*0.52 = 546,

By using R, test output is given as below:

> prop.test(x=c(250,546), n=c(600, 1050))

        2-sample test for equality of proportions with continuity correction

data: c(250, 546) out of c(600, 1050)

X-squared = 15.917, df = 1, p-value = 6.619e-05

alternative hypothesis: two.sided

95 percent confidence interval:

-0.1543351 -0.0523316

sample estimates:

   prop 1    prop 2

0.4166667 0.5200000

P-value for above test is given as 0.000066 approximately.

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that there is a statistically significant difference in two population proportions.