Question

In Houston,Texas a random sample of 400 adults were chosen to study the relationship between being religious and participating in the presidential election. 140 out of 200 religious people voted. 40 out of 100 non-religious people voted. Calculate a z-statistic for the difference between proportions. State the critical value. Let it be a two-tailed test where α= 0.05. And come to a conclusion about the difference between proportions.

Answer 1

Let P1 be the proportion of religious people who voted.

Let P2 be the proportion of non-religious people who voted.

Here we want to test

vs

Test statistic is

where

Here n1 = 200

n2 = 100

x1 = 140

x2 = 40

So

So

Here the test is two-tailed and the level of significance is 0.05.

So critical value is 1.96

Conclusion: As calculated test statistic is less than the level of significance we do not reject H0 and conclude that

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