In a clinical trial of Nasonex, 300 allergy patients were randomized into two groups, with Group 1 receiving the Nasonex drug (200 mg) and Group 2 receiving a placebo. The experimenter used a 2:1 randomization plan so that more subjects would be assigned to the Nasonex group. One outcome of interest is the incidence rate of headache as a side-effect. Of the 200 patients randomized to the Nasonex group, 52 (or 26%) reported experiencing a headache; and of the 100 patients randomized to the placebo group, only 22 (22%) reported a headache. 

a. A researcher plans to make a 95% confidence interval to estimate the difference in the headache rates for the population of all Nasonex patients versus population of all placebo patients. To use the multiplier of z* = 1.96, it must be determined if the sample sizes are large enough. This verification is slightly different than that for conducting a test of hypotheses. Provide sufficient verification for the use normality to construct the confidence interval.

b.
In the calculation of the confidence interval, we need to obtain the standard error of 1 – 2. Provide that standard error.

C. Provide the 95% confidence interval to estimate p1 – p2, the difference in the headache rates for the population of all Nasonex patients versus the population of all placebo patients. (1.5 pts)

D. Based on the interval, at a 5% significance level, does there appear to be a significant difference in the headache rates for the two populations of all Nasonex patients versus the population of all placebo patients? State your answer as yes or no and then provide a brief rationale for your answer.