A polical analyst wanted to find out if younger adults were

A polical analyst wanted to find out if younger adults were becoming more conservative. She decided to see if the mean age of registered Republicans was lower than registered Democrats. She selected an SRS of 128 registered Republicans and determined the mean age to be 39 years with a standard deviation of 8 years. She also selected an SRS of 200 Democrats and determined the mean age to be 40 years with a standard deviation of 10 years. Let

Solution

Given a=1-0.9=0.1, Z(0.05) = 1.645 (from standard normal table)

So the lower bound is

(xbar1-xbar2) - Z*sqrt(s1^2/n1+s2^2/n2)

=(39-40)-1.645*sqrt(8^2/128+10^2/200)

=-2.645

SO the upper bound is

(xbar1-xbar2) + Z*sqrt(s1^2/n1+s2^2/n2)

=(39-40)+1.645*sqrt(8^2/128+10^2/200)

=0.645

Answer: B) (-2.66, 0.66)