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: ₁ = 43 years and ₂ = 45 years. Assume that $\sigma$₁ = 5 and $\sigma$₂ = 8. Assuming a two-tail test and $\alpha$ = .05,the observed z value is _________________. A) -2.12 B) -2.25 C) -5.58 D) -15.38 E) -20.68

Question

Quizplus · Accepted Answer

The observed z-value is given by:

z = (x1 - x2) / sqrt(σ1^2/n1 + σ2^2/n2)

where x1 and x2 are the sample means, σ1 and σ2 are the population standard deviations, and n1 and n2 are the sample sizes.

Plugging in the values, we get:

z = (45 - 43) / sqrt(5^2/100 + 8^2/100) = -2.12

Since this is a two-tail test and the significance level is 0.05, we need to find the critical z-value. Using a z-table or calculator, we find that the critical z-value is ±1.96.

Since the observed z-value of -2.12 is less than the critical z-value of -1.96, we reject the null hypothesis and conclude that there is a significant difference in the ages of the audiences for American Idol and 60 Minutes.

Lucy Baker Is Analyzing Demographic Characteristics of Two Television Programs,American σ\sigmaσ

Lucy Baker Is Analyzing Demographic Characteristics of Two Television Programs,American $\sigma$