Question

You obtain 561 successes in a sample of size n1=672 from the first population. You obtain 522 successes in a sample of size n2=675 from the second population. Suppose that all assumptions are met, so that the difference in sample proportions follows a normal distribution. What is the test statistic for this sample?

Answer 1

The test statistic for the difference in sample proportions is calculated using the proportions from both populations and the standard error of the difference. It is represented by the formula (p1 - p2) / SE.

Step-by-step explanation:

To calculate the test statistic for the difference in sample proportions, you first need to find the sample proportions and then the standard error of the difference in sample proportions. For the first population, with 561 successes out of 672, the sample proportion is 561/672 = 0.8348. For the second population, with 522 successes out of 675, the sample proportion is 522/675 = 0.7733.

The formula for the test statistic is (p1 - p2) / SE, where SE is the standard error of the difference in sample proportions, calculated as sqrt((p1 * q1 / n1) + (p2 * q2 / n2)). In this scenario, q1 = 1 - p1 and q2 = 1 - p2. Therefore, SE = sqrt((0.8348 * 0.1652 / 672) + (0.7733 * 0.2267 / 675)). Finally, the test statistic is (0.8348 - 0.7733) / SE.