Question

10. Two different simple random samples are drawn from two different populations. The first sample consists of 40 people with 21 having a common attribute. The second sample consists of 1800 people with 1271 of them having the same common attribute. Compare the results from a hypothesis test of p 1=p  2 ​(with a 0.05 significance​ level) and a 95​% confidence interval estimate of p 1-p 2.

What are the null and alternative hypotheses for the hypothesis​ test?

A.H 0​: p 1 = p 2

H 1​: p 1 > p 2

B.H 0​: p 1 ≥ p 2

H 1​: p 1 ≠ p 2

C.H 0​: p 1 = p 2

H 1​: p 1 ≠ p 2

D.H 0​: p 1 ≤ p 2

H 1​: p 1 ≠ p 2

E.H 0​: p 1 ≠ p 2

H 1​: p 1 = p 2

F.H 0​: p 1 = p 2

H 1​: p 1 < p 2

Identify the test statistic.

______

​(Round to two decimal places as​ needed.)

Identify the critical​ value(s).

______

​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)

What is the conclusion based on the hypothesis​ test?

The test statistic is (not in/in) the critical​ region, so (fail to reject/reject) the null hypothesis. There is (insufficient/sufficient) evidence to conclude that p 1 ≠ p 2.

The 95​% confidence interval is___<(p1-p2)<____

​(Round to three decimal places as​ needed.)

What is the conclusion based on the confidence​ interval?

Since 0 is (included/not included) in the​ interval, it indicates to (reject/fail to reject) the null hypothesis.

How do the results from the hypothesis test and the confidence interval​ compare?

The results are (the same/different), since the hypothesis test suggests that p 1(greater than or equals/greater than/equals/less than or equals/not equals/less than)p 2​, and the confidence interval suggests that p 1(less than/equals/greater than/not equals/greater than or equals/less than or equals) p 2.

Answer 1

The test statistic is (not in) the critical​ region, so (reject) the null hypothesis. There is (sufficient) evidence to conclude that p 1 ≠ p 2.

Since 0 is (not included) in the​ interval, it indicates to (reject) the null hypothesis.

The results are (the same), since the hypothesis test suggests that p 1(/equals/)p 2​, and the confidence interval suggests that p 1(less than) p 2.