Question

The drug erythromycin has been proposed to lower the risk of premature
delivery. However, there are possible side effect of nausea when the drug is taken during pregnancy.
We want to estimate the incidence rate ?? of nausea during pregnancy, and we collect the 100 women
sample who are taking erythromycin regularly during weeks 24 and 28 of pregnancy, 90 of them
complained of nausea.
(a) [2 Points] Based on the sample, calculate the value of the point estimator of incidence rate ??.
(b) [4 Points] Please construct a 97% Confidence Interval for the incidence rate ??.
(c) [4 Points] Is (0.8415,0.9786) also a 97% confidence interval for the incidence rate ?? or Will
(0.8415,0.9786) have 97% contain the unknown true incidence rate ??? Why?
(d) [4 Points] Compare the confidence interval in Part (b) and Part (c), what’s the difference between
these two confidence intervals? Why we commonly use Symmetry setting in confidence interval?
Suppose that 75% of typical pregnant women (without taking erythromycin) complain of nausea
between weeks 24 and 28 of pregnancy.
(e) [4 Points] Test the hypothesis that the incidence rate ?? of nausea for the erythromycin group is
higher than the incidence rate for a typical pregnant woman at α = 5%.
(f) [5 Points] For reconfirm the result, we collect a new sample of 10 women during weeks 24 and 28
of pregnancy and find that all of them complain of nausea. Test the hypothesis that the incidence
rate ?? of nausea for the erythromycin group is higher than the incidence rate for a typical pregnant
woman based on the new sample at α = 5%. Hints: Use exact method and calculate its p-value.

Answer 1