Question

You wish to test the following claim ( H a ) at a significance level of α = 0.01 . H o : p 1 = p 2 H a : p 1 > p 2 You obtain 87.5% successes in a sample of size n 1 = 783 from the first population. You obtain 82% successes in a sample of size n 2 = 306 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution. What is the critical value for this test? (Report answer accurate to three decimal places.) critical value = What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = The test statistic is... in the critical region not in the critical region This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the first population proportion is greater than the second population proportion. There is not sufficient evidence to warrant rejection of the claim that the first population proportion is greater than the second population proportion. The sample data support the claim that the first population proportion is greater than the second population proportion. There is not sufficient sample evidence to support the claim that the first population proportion is greater than the second population proportion.

Answer 1

The statistical software output for this problem is:

Hence,

Critical value = 2.326

Test statistic = 2.348

The test statistic is in the critical region

Reject the null

The sample data support the claim that the first population proportion is greater than the second population proportion.