Question

Lucy Baker is analyzing demographic characteristics of the American Idol program. Previous studies indicate that the average viewer is 43 years old. May changes took place in the program and there are rumors the audience has changed. Mrs. Baker was tasked to find out . She randomly selects 100 people from the audience, and reports that the average age is 45 years. Assuming that variability in the ages of viewers is σ = 5 years, identify if Mrs. Baker's conclusion. She wants to accept a Type I error of .05.

Answer 1

We conclude that the mean age of average viewer has changed

Explanation:

H0 : μ = 43

H1 : μ > 43

The test statistic :

(xbar - μ) ÷ σ/sqrt(n)

Sample size, n = 100

xbar = 45 ; σ = 5

Test statistic :

(45 - 43) ÷ 5/sqrt(100)

2 ÷ 0.5 = 4

The Pvalue :

P(Z < 4) = 0.000032

Pvalue < α

0.000032 < 0.05 ; Hence, we reject the Null

We conclude that the mean age of average viewer has changed