Question

Umbrella Corporation is trying to determine whether a new drug improves mood in individuals with bipolar disorder. The company gave the drug to 220 individuals (Group 1) and a placebo (or sugar pill) to a separate sample of 280 individuals (Group 2). After one month on the drug, 186 of the patients in Group 1 reported improved mood, while 103 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.

I am really confused on how to work this out. Please show step by step for business analysis 3363 homework

Answer 1

Answer)

P1 = 186/220

P2 = 103/280

N1 = 220 and N2 = 280

Now, we need to check the conditions of normality, that is, if n1*p1 and n2*p2 both are greater than 5 or not.

N1*p1 = 186

N2*p2 = 103

As both are greater than 5, conditions are met so, we can use standard normal z table to estimate the interval.

From z table, critical value z for 99% confidence level is 2.58

Margin of error (MOE) = Z*Standard error

Standard error = √p1*(1-p1)/√n1 + √p2*(1-p2)/√n2

MOE = 0.0973726370258

Confidence interval is given by

(P1-p2)-MOE < (P1-P2) < (P1-P2)+MOE

0.3802247655715<(P1-P2)<0.5749700396232

0.3802<(p1-p2)<0.5750