Question

Umbrella Corporation is trying to determine whether a new drug improves mood in individuals with bipolar disorder. The company gave the drug to 270 individuals (Group 1) and a placebo (or sugar pill) to a separate sample of 234 individuals (Group 2). After one month on the drug, 157 of the patients in Group 1 reported improved mood, while 187 of the patients in Group 2 reported the same. Calculate the upper bound of a 99% confidence interval for the true difference in the proportion of individuals who experienced improved mood, to two decimal places. Take all calculations to four (4) decimal places.

Answer 1

Given that,

For Group 1 : n1 = 270, x1 = 157 and

For Group 2 : n2 = 234, x2 = 187 and

A 99% confidence level has significance level of 0.01 and critical value is,

The 99% confidence interval for the the true difference in the proportion of individuals who experienced improved mood is,

Where, lower bound = -0.32 and

Upper bound = -0.12