Question

You wish to test the following claim (H) at a significance level of a - 0.005. Ha:PI P2 You obtain 41.8% successes in a sample of size n2 536 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 distribrn sarmple of size ni = 694 from the first population. You obtain 31% successes in a What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic- What is the p-value for this sample? (Report answer accura to four decimal places.) p-value- The p-value is... O less than (or equal to)a greater than α This test statistic leads to a decision to... Oreject the null Oaccept the null Ofail to reject the null As such, the final conclusion is that.. OThere is sufficient evidence to warrant rejection of the claim that the first population proportion is greater than the second population proportion.

Answer 1

(a)

Data:

n1 = 694

n2 = 536

p1 = 0.418

p2 = 0.31

Hypotheses:

Ho: p1 ≤ p2

Ha: p1 > p2

Decision Rule:

α = 0.005

Critical z- score = 2.575829304

Reject Ho if z > 2.575829304

Test Statistic:

Average proportion, p = (n1p1 + n2p2)/(n1 + n2) = (694 * 0.418 + 536 * 0.31)/(694 + 536) = 0.370936585

q = 1 - p = 1 - 0.370936585365854 = 0.629063415

SE = √[pq * {(1/n1) + (1/n2)}] = √(0.370936585365854 * 0.629063414634146 * ((1/694) + (1/536))) = 0.027777137

z = (p1 - p2)/SE = (0.418 - 0.31)/0.0277771365990409 = 3.888

(b)

p- value = 0.0001

(c)

p- value ≤ α

(d)

Reject Ho and accept Ha

(e)

There is sufficient evidence that p1 > p2