Question

Randomly selected 80 student cars have ages with a mean of 8 years and a standard deviation of 3.6 years, while randomly selected 95 faculty cars have ages with a mean of 5.4 years and a standard deviation of 3.7 years.
1.    Use a 0.03 significance level to test the claim that student cars are older than faculty cars.
The test statistic is  
The critical value is  
Is there sufficient evidence to support the claim that student cars are older than faculty cars?

A. Yes
B. No

2.    Construct a 97% confidence interval estimate of the difference μ1−μ2, where μ1 is the mean age of student cars and μ2 is the mean age of faculty cars. ____ <(?1−?2)< ____

Answer 1

Ans:

Assumption:population variances are not equal.

1)

Test statistic:

t=(8-5.4)/sqrt((3.6^2/80)+(3.7^2/95))

t=4.70

df=80-1=79

critical t value=1.908

Yes,there is sufficient evidence to support the claim that student cars are older than faculty cars.

2)97% confidence interval estimate for difference

=(8-5.4)+/-2.210*sqrt((3.6^2/80)+(3.7^2/95))

=2.6+/-1.22

=(1.38, 3.82)