Proportions Suppose we wish to test whether an allergy drug

Proportions Suppose we wish to test whether an allergy drug has an equal success rate with men and women. From a sample of 102 men and 94 women we find that 66 men and 47 women report alleviated symptoms. Create a 95% confidence interval for the true difference in the proportion of men and women who experience relief. (Here use men-women and be careful to leave proportions as fractions!): Note: Answer using 3-decimal precision Low = 1 to High =

Solution

CI = (p1 - p2) ± Z a/2 Sqrt(p1(1-p1)/n1 + p2(1-p2)/n2 )
Proportion 1
Probability Succuses( X1 )=66
No.Of Observed (n1)=102
P1= X1/n1=0.64706
Proportion 2
Probability Succuses(X2)=47
No.Of Observed (n2)=94
P2= X2/n2=0.5
C.I = (0.64706-0.5) ±Z a/2 * Sqrt( (0.64706*0.35294/102) + (0.5*0.5/94) )
=(0.64706-0.5) ± 1.96* Sqrt(0.0049)
=0.14706-0.13718,0.14706+0.13718
=[0.00988,0.28424] ~ 0.988% to 28.424% OR ROUNDING OFF to 3 PRECCISON[ 0.01, 0.284]