Question

Q6 Given two independent random samples with the following results:

n1ˆ=552   p1=0.66

???n2=462 p2 =0.86

Can it be concluded that the proportion found in Population 2 exceeds the proportion found in Population 1?  Use a significance level of ?=0.05 for the test.

Step 1 of 5: State the null and alternative hypotheses for the test.

Step 2 of 5:Compute the weighted estimate of p, p?? Round your answer to three decimal places.

Step 3 of 5: Compute the value of the test statistic. Round your answer to two decimal places.

Step 4 of 5: Find the P-value for the hypothesis test. Round your answer to four decimal places.

Step 5 of 5:Make the decision to reject or fail to reject the null hypothesis.

a. Fail to reject the null hypothesis. There is not sufficient evidence, at the 0.05 level of significance, that the proportion for Population 2 exceeds the proportion for Population 1

b. Fail to reject the null hypothesis. There is sufficient evidence, at the 0.05 level of significance, that the proportion for Population 2 exceeds the proportion for Population 1

c. Reject the null hypothesis. There is sufficient evidence, at the 0.05 level of significance, that the proportion for Population 2 exceeds the proportion for Population 1.

d. Reject the null hypothesis. There is not sufficient evidence, at the 0.05 level of significance, that the proportion for Population 2 exceeds the proportion for Population 1.

Answer 1

1)

H0 : p1 = p2
Ha : p1 < p2

2)

p = (p1 * n1 + p2 * n2) / (n1 + n2)

= (0.66 * 552 + 0.86 * 462)/(552 + 462)

= 0.7511

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
= sqrt( 0.7511 *(1-0.7511) *((1/552) + ( 1/462)))
= 0.0273

3)

z = (p1 - p2) / SE
= (0.66 - 0.86)/0.0273
= -7.3260

4)

p value = 0.00001

5)
c. Reject the null hypothesis. There is sufficient evidence, at the 0.05 level of significance, that the proportion for Population 2 exceeds the proportion for Population 1