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 your conclusion in the context of the problem?

Answer 1

Answer)

Null hypothesis Ho : P1 = P2

Alternate hypothesis Ha : P1 > P2

N1 = 103, P1 = 28/103

N2 = 374, P2 = 69/374

First we need to check the conditions of normality that is if n1p1 and n1*(1-p1) and n2*p2 and n2*(1-p2) all are greater than equal to 5 or not

N1*p1 = 28

N1*(1-p1) = 75

N2*p2 = 69

N2*(1-p2) = 305

All the conditions are met so we can use standard normal z table to conduct the test

Test statistics z = (P1-P2)/standard error

Standard error = √{p*(1-p)}*√{(1/n1)+(1/n2)}

P = pooled proportion = [(p1*n1)+(p2*n2)]/[n1+n2]

After substitution

Test statistics z = 1.95

From z table, P(Z > 1.95) = 0.0256

So, P-Value = 0.0256

As the obtained P-Value is less than the given significance (0.05)

We reject the null hypothesis Ho

So we have enough evidence to conclude that the depressed (D) patients with cardiac disease are more likely to die than non-depressed (ND) patients with cardiac disease