Umbrella Corporation is trying to determine whether a new drug improves mood in
ID: 3243423 • Letter: U
Question
Umbrella Corporation is trying to determine whether a new drug improves mood in individuals with bipolar disorder. The company gave the drug to 261 individuals (Group 1) and a placebo (or sugar pill) to a separate sample of 260 individuals (Group 2). After one month on the drug, 195 of the patients in Group 1 reported improved mood, while 125 of the patients in Group 2 reported the same. Calculate the lower bound of a 95% confidence interval for the true difference in the proportion of individuals who experienced improved mood, to two decimal places.
Explanation / Answer
n1 = 261
n2 = 260
p1 = 0.747126437
p2 = 0.480769231
% = 95
Pooled Proportion, p = (n1 p1 + n2 p2)/(n1 + n2) = (261 * 0.747126436781609 + 260 * 0.480769230769231)/(261 + 260) = 0.614203455
q = 1 - p = 1 - 0.614203454894434 = 0.385796545
SE = (pq * ((1/n1) + (1/n2))) = (0.614203454894434 * 0.385796545105566 * ((1/261) + (1/260))) = 0.042652769
z- score = 1.959963985
Width of the confidence interval = z * SE = 1.95996398454005 * 0.0426527687967245 = 0.083597891
Lower Limit of the confidence interval = (p1 - p2) - width = 0.266357206012378 - 0.0835978906824939 = 0.18
Upper Limit of the confidence interval = (p1 - p2) + width = 0.266357206012378 + 0.0835978906824939 = 0.35.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.