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

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!

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

To calculate the 95% confidence interval for the difference in the chance of death due to a heart attack between the placebo and aspirin groups, you need to follow these steps:

1. Calculate the sample proportions for each group:
- Placebo group: 28 out of 684 patients died (proportion = 28/684 = 0.041)
- Aspirin group: 18 out of 676 patients died (proportion = 18/676 = 0.027)

2. Calculate the standard error of the difference in proportions:
- SE = sqrt[(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)]
- Where p1 and p2 are the sample proportions, n1 and n2 are the sample sizes.
- In this case, p1 = 0.041, p2 = 0.027, n1 = 684, n2 = 676.

3. Calculate the margin of error:
- MOE = z * SE
- Where z is the z-score corresponding to the desired confidence level.
- In this case, for a 95% confidence level, z = 1.96.

4. Calculate the confidence interval:
- Confidence interval = (p1 - p2) ± MOE

Now, let's calculate the values:

1. Sample proportions:
- Placebo group: p1 = 0.041
- Aspirin group: p2 = 0.027

2. Standard error of the difference in proportions:
- SE = sqrt[(0.041 * (1 - 0.041) / 684) + (0.027 * (1 - 0.027) / 676)]

3. Margin of error:
- MOE = 1.96 * SE

4. Confidence interval:
- Lower bound = (0.041 - 0.027) - MOE
- Upper bound = (0.041 - 0.027) + MOE

The calculated confidence interval will give you the range within which the true difference in the chance of death due to heart attack between the two groups is likely to lie with 95% confidence.