A social scientist is interested in determining if there is a significant difference in the proportion of Republicans between two areas of town. He takes independent random samples of 200 families in each area of town and a significance test was conducted. The p-value was 0.0156. What should be our conclusions?

Testing the hypothesis, it can be concluded that since the p-value is of 0.0156 < 0.05, the proportion of Republicans between two areas of town is different.

At the null hypothesis, we test if the proportions are the same, that is:

At the alternative hypothesis, we test if the proportions are different, that is:

The p-value is of 0.0156, which is less than the standard significance level of 0.05, hence the null hypothesis is rejected, and it can be concluded that the proportions are different.

A similar problem is given at link

Given

p-value = 0.0156

n = 200 families

Our conclusion goes as follows:

The statistical evidence is pretty strong enough to conclude that there is a difference in the proportion of Republicans between the two areas of town because we know that small p­-value indicates significant differences, and a p­value of 0.0156 is pretty small to ascertain our conclusion.