Question

Lucy Baker is analyzing demographic characteristics of two television programs, American Idol (population 1) and 60 Minutes (population 2). Previous studies indicate no difference in the ages of the two audiences. (The mean age of each audience is the same.) Her staff randomly selected 100 people from each audience, and reported the following: sample mean for population 1 = 43 years and sample mean for population 2 = 45 years. Assume that σ 1 = 5 and σ 2 = 8. With a two-tail test and α = .05, the appropriate decision is

Answer 1

Null Hypothesis H0: True mean difference in age of audiences of American Idol and 60 Minutes is zero.

Alternative Hypothesis Ha: True mean difference in age of audiences of American Idol and 60 Minutes is not zero.

Since we know the population standard deviations of groups, we will conduct two sample z test.

Standard error of mean difference = = 0.9433981

Test statistic, z = / SE

= |43 - 45| / 0.9433981

= 2.12

For two tail test, p-value = 2 * P(z > 2.12) = 0.034

Since, p-value is less than 0.05 significance level, we reject null hypothesis H0 and conclude that there is strong evidence that mean difference in age of audiences of American Idol and 60 Minutes is not zero. There is significant differences in true mean age of audiences of American Idol and 60 Minutes at 0.05 significance level.