Question

A study examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among the patients who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? a. Write appropriate hypotheses. b. Test your hypothesis and state your conclusion. c. Explain in this context what your P-value means. d. If your conclusion is actually incorrect, which type of error did you commit?

Answer 1

a) The hypotheses

H0 : p1=p2

Ha: p1 < p2

where p1 is the proportion of cardiac patients with no depression dies

where p2 is the proportion of cardiac patients with depression dies

b) Test statistic

where

P= 0.2067

Q= 0.7933

z = -2.22

P value = 0.0132 ( one tailed)

Since P value < 0.05 , the result is significant

We reject H0.

There is sufficient evidence to conclude that among cardiac patients , depressed ones are more likely to die than non depressed ones.

c) P value is the probability of getting  proportion of depressed patients dying more than proportion of non depressed ones when we assume that there is no difference between  proportion of depressed patients dying and non depressed patients dying.

d) we reject the null hypothesis

therefore we may have committed type 1 error , which is the probability of rejecting a true null hypothesis .

That is we might have wrongfully concluded that  depressed ones are more likely to die than non depressed one when in reality there may be no significant difference between  proportion of depressed patients dying and non depressed patients dying.