A Swedish study used 1360 patients who had suffered a stroke. The study

Question

randomly assigned 684 patients to receive a placebo treatment and the rest to receive an
aspirin treatment. Out of those who received the placebo treatment, 28 died due to heart
attack in 3 years, whereas 18 of those who received the aspirin treatment died due to heart
attack in the same period.
Obtain a 95% confdence interval for the difference in the chance of death due to heart
attack between the two groups.

So for the placebo group n=684 and 28 died so the proportion that died is 0.041.
For the aspirin group n= 676 and 18 died. So the proportion that died is 0.027.

Since we're looking for the 95% confidence level the zscore would be 1.96.

I'm not sure how I would find the standard deviation though.
But once I have a value for the standard deviation I could find the margin of error and the interval for the chance of death.

Or do we even need to find the SD for this question?
I was also thinking I might have to calculate the probabilty of someone dying in either group? But I'm not sure how to do this. And does the fact that the patients died within 3 years have any relevance?

Thanks for your help!

Answer 1

use test for proportions :

Formula : ( p1 - p2 ) / sqrt ( Pcap * Q cap ( 1/n1 + 1/n2 )

where P cap = (n1p1 + n2p2 )/ (n1 + n2 )
Q cap = 1 - P cap