FIND THE LOWER LIMIT AND UPPER LIMIT In the Health ABC Study

FIND THE LOWER LIMIT AND UPPER LIMIT

In the Health ABC Study, 535 subjects owned a pet and 1973 subjects did not. Among the pet owners, there were 290 women; 989 of the non-pet owners were women. Find the proportion of pet owners who were women. Do the same for the non-pet owners. Give a 90% confidence interval for the difference in the two proportions. (Be sure to let Population 1 correspond to the group with the higher proportion so that the difference will be positive.)

Solution

CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Number of women owns a pet(x)=290
Sample Size(n)=989
Sample proportion = x/n =0.2932
Confidence Interval = [ 0.2932 ±Z a/2 ( Sqrt ( 0.2932*0.7068) /989)]
= [ 0.2932 - 1.64* Sqrt(0.0002) , 0.2932 + 1.64* Sqrt(0.0002) ]
= [ 0.2695,0.3169]