Question

You wish to test the following claim ( H a H a ) at a significance level of α = 0.10 α = 0.10 . H o : p 1 = p 2 H o : p 1 = p 2 H a : p 1 > p 2 H a : p 1 > p 2 You obtain 432 successes in a sample of size n 1 = 681 n 1 = 681 from the first population. You obtain 263 successes in a sample of size n 2 = 456 n 2 = 456 from the second population. 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 accurate to four decimal places.) p-value = The p-value is... less than (or equal to) α α greater than α α 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

p1 = 432/681 = 0.634
p2 = 263/456 = 0.577

pcap = (432 + 263)/(681+456) = 0.6113

z = (p1 -p2)/sqrt(pcap*(1-pcap) *(1/n1+1/n2))
= ( 0.634 - 0.577)/sqrt(0.6113 *(1-0.6113) *(1/681 + 1/456))
= 1.9530

p value = .0254

The p-value is.less than (or equal to) α α greater than α This test statistic leads to a decision 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