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.With a two-tail test and $\alpha$ = .05,the critical z values are _________________.
A)-1.64 and 1.64
B)-1.96 and 1.96
C)-2.33 and 2.33
D)-2.58 and 2.58
E)-2.97 and 2.97

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:  1 = 43 years and  2 = 45 years.Assume that  $\sigma$1 = 5 and  $\sigma$2 = 8.With a two-tail test and $\alpha$ = .05,the critical z values are _________________.
A)-1.64 and 1.64 
B)-1.96 and 1.96 
C)-2.33 and 2.33 
D)-2.58 and 2.58 
E)-2.97 and 2.97

Quizplus · Accepted Answer

Since it is a two-tail test with α = .05, we need to split the α level in half and place it in both tails of the distribution, which gives us α/2 = .025. Looking up the critical z values for a .025 area in each tail of the distribution, we find the values of -1.96 and 1.96. Therefore, the correct answer is choice B.

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

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