Question

A study is conducted to investigate the impact of depression on a patient’s ability to survive cardiac disease. They evaluated 477 participants for depression and followed for 4 years. There were 374 patients with no depression (ND) and 69 of them died. Out of 103 patients with minor or major depression (D), 28 died. Does it appear that the depressed (D) patients with cardiac disease are more likely to die than non-depressed (ND) patients with cardiac disease?
Conduct a test of hypothesis at 5% level of significance.

What is the p-value for the test?

Answer 1

let p1 and p2 are population proportion for  depressed (D) and  no depression (ND) patients who  die with cardiac disease

P:-P2 null Hypothesis: Ho: alternate Hypothesis: Ha: 0.0000 0.0000 P1-P2 1.645 for 0.05 level with right tailed test, critical value of z= Decision rule: reject Ho if test statistic z > 1.645 ND 69 Pz=xz/n, = 28 P:=xg/n = 0.2718 103 estimated difference in proportion =P:-P2 estimator of pooled proportion p =(x2+xz)/(n2+nz) 0.1845 374 0.0874 0.2034 std error Se= VlP1*(1-.)*(1/n4+1/nz) 0.0448 test stat z = (P-2)/Se 1.95 P value = 0.0256

from above p value =0.0256

as p value is less than 0.05 we reject null and conclude that  patients with cardiac disease are more likely to die than non-depressed (ND) patients with cardiac disease