This is the question i am having issues with, if anyone is keen to help, i'd really appreciate it.
Two groups, A and B, consist of people with a disease. Each group was randomly selected from a large number of patients. A serum is given to Group A, while Group B receives a placebo. Otherwise the two groups are treated identically. In group A, 74 out of 108 people recover from the disease, while in group B, 61 out of 113 recover.
(a) Using a test statistic which has a normal distribution, test the hypothesis that the serum helps to cure the disease. Assume a 5% significance level.
(b) Calculate a 95% confidence interval for the difference in recovery rates between serum and placebo.
for a) the test stat i would use is:
and for b) i would use the 95% which is 1.96
and the formula for that would be
CI=(ρ ̂_1-ρ ̂_2)±k√((ρ ̂_1 (1-ρ ̂_1))/n_1 +(ρ ̂_2 (1-ρ ̂_2))/n_2 )