I'm taking a Statistics class but this question really boggles me.
100 people are given a standard antibiotic to treat infection and another 100 are given a new antibiotic. In the first group, 90 people recover; in the second group, 85 people recover. Let p1 be the probability of recovery with the standard antibiotic and p2 be the probability of recovery with the new antibiotic. We are interested in estimating θ= p1 −p2. Provide an estimate, standard error, an 80% confidence interval, and a 95% confidence interval for θ.
So from what I gathered p1 = 0.90 and p2 = 0.85. So θ= 0.90-0.85 = 0.05. However, I do not understand how I can find the SE (which will need SD) and the CI when I was only given a pair of probabilities to work on.
Please kindly shed light on this.
Thank you,