Marketers want to know about the differences between men\'s and women\'s use of
ID: 3156741 • Letter: M
Question
Marketers want to know about the differences between men's and women's use of the Internet. A research poll in April 2009 from a random sample of adults found that 2382 of 3001 men use the Internet, while 2373 of 3188 women did. a). Find the proportions of men and women who said they use the Internet at least occasionally. b). What is the difference in proportions? C). What is the standard error of the difference? d). Find a 95% confidence interval for the difference between percentages of usage by men and women nationwide.
Explanation / Answer
a) p1hat=2382/3001=0.7937 p2hat=2373/3188=0.7444, where p1hat and p2hat are proportion of men and women.
b) p1hat-p2hat=0.7937-0.7444=0.0493
c) SE(p1hat-p2hat)=sqrt [p1hat(1-p1hat)/n1+p2hat(1-p2hat)/n2]
=sqrt[0.7937(1-0.7937)/3001+0.7444(1-0.7444)/3188]
=0.011
d) 95% c.i=(p1hat-p2hat)+-ZSE(p1hat-p2hat)
=0.0493+-1.96*0.011
=0.0277 to 0.0709