Question

Randomly selected 29 student cars have ages with a mean of 7.3 years and a standard deviation

of 3.6 years, while randomly selected 20 faculty cars have ages with a mean of 5.8 years and a
standard deviation of 3.5 years. Assume the populations are normal.
I. 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. No B. Yes
2. Construct a 95% confidence interval estimate of the difference us—gf, where us is the mean
age of student cars and I-If is the mean age of faculty cars.

Answer 1

To test the claim that student cars are older than faculty cars, a two-sample t-test with a significance level of 0.05 is used. The test statistic is calculated using the difference in means, standard deviations, and sample sizes. The critical value can be found in the t-distribution table. A confidence interval estimate of the mean difference can also be calculated.

Step-by-step explanation:

To test the claim that student cars are older than faculty cars, we can use a two-sample t-test with a significance level of 0.05. The test statistic can be calculated as:

t = (mean1 - mean2) / sqrt((s1^2/n1) + (s2^2/n2))

where mean1 and mean2 are the means of the student car ages and faculty car ages, s1 and s2 are the standard deviations, and n1 and n2 are the sample sizes.

The critical value can be found using the t-distribution table with (n1 + n2 - 2) degrees of freedom. If the calculated t-value is greater than the critical value, then we reject the null hypothesis and conclude that student cars are older than faculty cars.

For the confidence interval estimate, we can use the formula:

CI = (mean1 - mean2) ± tα/2 * sqrt((s1^2/n1) + (s2^2/n2))

where tα/2 is the critical value corresponding to the desired confidence level. In this case, a 95% confidence interval estimate of the difference between the mean ages of student cars and faculty cars can be computed.