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. The makers of Nasonex are concerned that their allergy medication might increase the incidence of headaches. So they would like to assess if the incidence rate of headaches is significantly higher for Nasonex users as compared to placebo (at the 5% level). So the null hypothesis is given by H0: p1 = p2. Select the appropriate alternative hypothesis.
i. Ha: p1 not equal to p2
ii. Ha: p1 > p2
iii. Ha: p1 < p2
B. It is important to understand what the various parameters in the hypotheses represent. Consider the following incorrect definition for the parameter p1.
"p1 is the proportion of Nasonex allergy patients in the sample who experience a headache". Provide the two words to complete this statement: This definition would be correct if you replace the word Sample with the word Population.
C. The test statistic is computed assuming the null hypothesis is true, that is, p1 = p2 = p. Which of the following is the best estimate of that common proportion p?
i. 0.1867
ii. 0.22
iii. 0.2467
iv. 0.26
D. It seems that the sample sizes of 200 and 100 should be sufficiently large enough to use a normal approximation to compute the p-value. Provide verification that the sample sizes are large enough.
E. Provide an estimate of the difference in the headache rates for the population of all Nasonex patients versus population of all placebo patients; that is, an estimate of p1 - p2.
i. 0.04
ii. 0.05
iii. 0.06
iv. 0.07
f.Which of the following is the corresponding test statistic for testing the hypotheses in part (a)?
i. 0.76
ii. 0.96
iii. 1.16
iv. 1.36
g.Find the corresponding p-value. Describe what the sketch would look like of this p-value.
H. At a 5% significance level, state your statistical decision (reject or fail to reject the null hypothesis) and then write a one sentence conclusion (in the context of the problem).