Question

(1 pt) Randomly selected 22 student cars have ages with a mean of 7.6 years and a standard deviation of 3.4 years, while randomly selected 10 faculty cars have ages with a mean of 5.4 years and a standard deviation of 3.5 years. 1. Use a 0.05 significance level to test the claim that student cars are older than faculty cars. (a) The test statistic is (b) The critical value is (c) Is there sufficient evidence to support the claim that student cars are older than faculty cars? A. Yes B. No 2. Construct a 95% confidence interval estimate of the difference μ,-8p where μ' is the mean age of student cars and μ1 is the mean age of faculty cars.

Answer 1

The value of the test static is  

The number of degrees of freedom is 22+10-2=20, the test is left tailed

So critical value is 1.725

Since 1.66< 1.725

So fail to reject the null hypothesis

No, there is not enough evidence to support the claim.

The interval is given by

$\left ( [7.6-5.4]- (2.086)\sqrt{{(3.4)^2\over 22}+{(3.5)^2\over 10}}~,~ [7.6-5.4] + (2.086)\sqrt{{(3.4)^2\over 22}+{(3.5)^2\over 10} } \right ) \\ \\ ~~~~~~\hspace{5cm}~~~=(-0.56~,~4.96)$