A political analyst was curious if younger adults were becom

A political analyst was curious if younger adults were becoming more conservative. He decided to see if the mean age of registered to the Liberal Party was lower than that of those registered to the Labour Party. He selected an SRS of 12 individuals registered to the Liberal Party and determined the mean age to be x1 = 39 years, with a standard deviation s1 = 8 years. He also selected an independent SRS of lo individuals registered to the Labour Party and determined the mean age to be x2-bar = 45 years, with a standard deviation s2 = 10 years. Let mu1 and mu2 represent the mean ages of the populations of all individuals registered to the Liberal Party and the Labour Party, respectively. Suppose that the distributions of age In the populations of registered Republicans and of registered Democrats have the same standard deviation. Suppose the researcher had wished to test the hypotheses H0: mu1 = mu2, H0 : mu1

Solution

Set Up Hypothesis
Null, Ho: u1 = u2
Alternate, - H1: u1 < u2
Test Statistic
X(Mean)=39
Standard Deviation(s.d1)=8 ; Number(n1)=12
Y(Mean)=45
Standard Deviation(s.d2)=10; Number(n2)=10
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =39-45/Sqrt((64/12)+(100/10))
to =-1.53
| to | =1.53

P-Value:Left Tail - Ha : ( P < -1.5323 ) = 0.07991

P-value is between 0.10 and 0.05