Problem 4.In clinical trials of Nasonex, 3774 adults and adolescent allergy patients (patients 12 years and older). Were randomly divided into two groups. The patients in group 1 (experimental group) received 200 g of Nasonex, while the patients in group 2 (Control group) received a placebo. Of the 2103 patients in the experimental group 647 reported headaches as a side effect. Of the 1671 patients in the control group, 468 reported headaches as a side effect.

1. Is there a significant difference to conclude that the proportion of Nasonex users that experienced headaches as a side effect is greater than the proportion in the control group at the =0.05 level of significance?
   • Assumption:
   • Hypotheses:
   • Test statistic: what is the distribution of test statistic? Based on the sample information provided in this problem, what is the value of the test statistic?
   • P-value
   • Refer to the conclusion from this Problem. Based on the conclusion (reject the null or fail to reject the null), what type of error (either Type 1 or type 2) could you have made? Explain.
2. Repeat this analysis in R. Hint: Use the prop.test() command
3. Construct by hand and interpret the 90% confidence interval for the difference between the two population proportions and interpret. Hint: Don't forget to check if the assumptions are met
4. Fond the 90% CI by using the prop.test() command in R