Having trouble with this problem, could you please explain thoroughly? Thanks in

Question

Having trouble with this problem, could you please explain thoroughly? Thanks in advance

A study was conducted to compare 2 types of high blood pressure drugs and their suspected link to cancer. One type, is called calcium-channel blockers and the other is called beta-blockers. A random sample of 202 elderly patients (sample 1) was selected from the population of elderly people taking calcium-channel blockers A random sample or 424 elderly patients (sample 2) was selected from the population of elderly people taking beta-blockers. Of the 202 patients taking calcium-channel blockers. 27 developed cancer. Of the 424 taking beta-blockers. 28 developed cancer. Test the claim that elderly patients who take calcium-channel blockers have a significantly higher rate of cancer than elderly patients who take beta-blockers. Use a 01 significance level. The alternative hypothesis is (enter choice 1, 2, or 3) p1 > p2 p1

Explanation / Answer

n1 =202 ,X1 = 27

n2 = 424 ,X2 = 28

alternate hypothesis

is p1 > p2

because we want to test if sample 1 has higher rate than thta of sample 2

p1^-p2^ = X1/n1 -X2/n2 = 27/202 - 28/424 = 0.0676256

pooled estimate = (x1 +x2)/(n1 +n2) = (27+28)/(202+424) =0.0878594

Z = (p1^-p2^)/(sqrt(pq*(1/n1+1/n2))

=(0.0676256)/(sqrt(0.0878594*(1/202+1/424))

=2.66863

z-critical = 1.645 for alpha = 0.05

since TS> critical value {2.66863> 1.645 }

we reject the null

there is significant evidence that p1 > p2

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