Question

A medical researcher conjectures that smoking can result in the wrinkled skin around the eyes. The researcher recruited 150 smokers and 250 nonsmokers to take part in an observational study and found that 95 of the smokers and 105 of the nonsmokers were seen to have prominent wrinkles around the eyes (based on a standardized wrinkle score administered by a person who did not know if the subject smoked or not). How do the smokers compare to the non-smokers? Find 95% Confidence intervals for the true difference in proportions between these two groups in the population

Answer 1

smokers ---1

nonsmokers -- 2

n1=150 , x1 = 95

n2= 250 ,x2 =105

p1= 95/150 = 0.6333

p2 = 105 /250 = 0.42

pooled

H0 : P1=P2

H1: P1 > P2

95% confidence interval for difference of proportion

{0.112086 , 0.314514} Answer

Also Z = 0.21333 / 0.0516398

   Z= 4.13

p value = 0.000018 < 0.05

Reject Ho

conclusion : P1 > P2