Marketers want to know about the differences between mens an

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 2396 of 3022 men use the Internet, while 2355 of 3192 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.

Solution

a. Proportion of men = 2396 / 3022 = 0.79

Proportion of women = 2355 / 3192 = 0.74

b. Difference in proportions = 0.79 - 0.74 = 0.05

c. Standard error = sqrt[(P * (1-P)] * sqrt[( 1 / n1) + 1 / n2)]

= sqrt[(0.76 * 0.24)] * sqrt[(1 / 3022) + (1 / 3192)] = 0.42 * 0.03 = 0. 01

where P = (2396 + 2355) / (3022 + 3192) = 0.76

d. 95% confidence interval = sample statistic -/+ margin of error = 1.96 * 0.01 = 0.0196

We are 95% confident that the true difference in population proportion is between 0.03 and 0.07 (0.05 -/+ 0.196)

alpha = 1 - 0.95 = 0.05

critical probability = 1 - alpha/2 = 0.975

critical value = 1.96