Question

You wish to test the following claim ( H a ) at a significance level of α = 0.002 . H o : p 1 = p 2 H a : p 1 ≠ p 2 You obtain 16.2% successes in a sample of size n 1 = 395 from the first population. You obtain 18.3% successes in a sample of size n 2 = 613 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. The test statistic's value is p ˆ 1 − p ˆ 2 √ p ˉ ⋅ ( 1 − p ˉ ) ⋅ ( 1 n 1 + 1 n 2 ) =(0.162 - 0.183)/sqrt(0.175*(1-0.175)*(1/395+1/613)) = -0.857.

1) What is the test statistic for this sample?

a.independent samples b. t-test c.z-test d.paired samples t-test

2) What is the p-value for this sample?

(Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) α greater than α

3) This test statistic leads to a decision to

A. reject the null B. fail to reject the null C.accept the null

4) As such, the final conclusion is that...

A. The sample data support the claim that the first population proportion is not equal to the second population proprtion.

B. There is not sufficient evidence to warrant rejection of the claim that the first population proportion is not equal to the second population proprtion

C. There is not sufficient sample evidence to support the claim that the first population proportion is not equal to the second population proprtion.

D. There is sufficient evidence to warrant rejection of the claim that the first population proportion is not equal to the second population proprtion.

Answer 1

(A) we are comparing to proportions and we know that we always use z test for comparing 2 proportions.

so, answer is z test

(B) given that z statistic = -0.857

using z table, check -0.8 in the row and 0.06 in the column

select the intersecting cell

we get

p value = 0.3914

p value is greater than alpha level

(C) we failed to reject the null hypothesis because the alpha level (0.02) is less than p value. So, result is insignificant.

(D) Result is insignificant, so we can say that there is insufficient evidence to conclude that the proportions are unequal.

option D is correct