Consider the following two groups of women: Group 1 - women who spend less than
ID: 3131081 • Letter: C
Question
Consider the following two groups of women: Group 1 - women who spend less than $500 annually for clothes; Group 2 - women who spend over $1000 annually for clothes. Let p1 and p2 equal the proportions of women in these two groups, respectively, who believe that clothes are too expensive. If 1009 out of a random sample of 1230 women from group 1 and 207 out of a random sample of 340 from group 2 believe that clothes are too expensive,
(a) Give a point estimate of p1 p2.
(b) Find an approximate 95% confidence interval for p1 p2.
Explanation / Answer
p1 = 1009 / 1230 = 0.8203
p2 = 207 / 340 = 0.6088
a)
p1 - p2 = 0.8203 - 0.6088 = 0.2115
b)
for alpha = 1 - 0.95 = 0.05
alpha / 2 = 0.025
Z=1.96 from tables of normal distribution standard
p1-p2 +/- Z * srqt ( p*q* (1/n1 + 1/n2) )
P = [1009+207 ] / [1230 + 340 ] = 0.7745
Q = 0.2255
0.2115 +/- 1.96 * SRQT ( 0.7745*0.2255 * ( 1/1230 + 1/340 ) )
0.2115 +/- 0.05019
0.16131 < p1-p2 < 0.26169