Question

You wish to test the following claim (Ha ) at a significance level of . 0.01 You obtain a sample from the first population with 163 successes and 292 failures. You obtain a sample from the second population with 248 successes and 409

failures. What is the test statistic for this sample

Answer 1

The test statistic for this sample is -0.7308.

Step-by-step explanation:

The test statistic for this sample can be calculated using the formula for the two-sample test for proportions.

First, calculate the sample proportions for each sample.

For the first sample, the proportion of successes is 163/455 = 0.358

For the second sample, the proportion of successes is 248/657 = 0.377

Next, calculate the standard error using the formula sqrt((p1*(1-p1))/n1 + (p2*(1-p2))/n2), where p1 and p2 are the sample proportions and n1 and n2 are the sample sizes.

In this case, the standard error is sqrt((0.358*(1-0.358))/455 + (0.377*(1-0.377))/657) = 0.026

Finally, calculate the test statistic using the formula (p1 - p2) / standard error.

In this case, the test statistic is (0.358 - 0.377) / 0.026 = -0.7308