Randomly selected $14$ student cars have ages with a mean of $7.6$ years and a standard deviation of $3.4$ years, while randomly selected $27$ faculty cars have ages with a mean of $6$ years and a standard deviation of $3.5$ years.

1. Use a $0.01$ 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 $99$% confidence interval estimate of the difference $\mu_s - \mu_f$, where $\mu_s$ is the mean age of student cars and $\mu_f$ is the mean age of faculty cars.
$< (\mu_s - \mu_f) <$