Question

Given two independent random samples with the following results: n1 =685, p1=0.5, n2 =510, p2 =0.67. Can it be concluded that the proportion found in population 2 exceeds the proportion found in population 1? Find the p-value for the hypothesis test. Make the decision for the hypothesis test.

Answer 1

As we are testing here whether proportion found in population 2 exceeds the proportion found in population 1 ,

the pooled proportion here is computed as:

The standard error now is computed here as:

The test statistic here is computed as:

As the test statistic value here is very high, therefore the p-value : P(Z > 5.8765) = approx 0. Therefore the test is significant here and we can reject the null hypothesis here and conclude that the proportion found in population 2 exceeds the proportion found in population 1