Question: Two groups, A and B, consist of 100 people each who have a disease. A serum is given to group A but not to group B (which is called the control group); otherwise, the two groups are treated identically. It is found that in groups A and B, 75 and 65 people respectively, recover from the disease.

1. At a significance level of a = 0.01, test the hypothesis that the serum helps cure the disease.
2. Now assume that each of the groups consists of 300 people, respectively, and that 225 people in group A and 195 people in group B are cured (the same proportion of cured patients as in part a). At a significance level of α = 0.01, again test the hypothesis that the serum helps cure the disease.
3. Are your results consistent in parts a and b, please explain.

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