Question

In: Statistics and Probability

A random sample 11 student cars (group 1) were found to have ages with a mean...

A random sample 11 student cars (group 1) were found to have ages with a mean of 7 years and a standard deviation of 3.4 years, while second, independent random sample of 10 faculty cars (group 2) were found to have ages with a mean of 5.2 years and a standard deviation of 3.5 years. You may assume that car ages for both groups are approximately normally distributed and that the two population variances are equal.

1. Use a 0.01 significance level to test the claim that, on average, student cars are older than faculty cars.

(a) The test statistic is t =

(b) The critical value is t =

(c) Is there sufficient evidence to support the claim that student cars are older than faculty cars?

A. No B. Yes

Solutions

Expert Solution

H0:

H1:

a) The test statistic t = ()/sqrt(s1^2/n1 + s2^2/n2)

                               = (7 - 5.2)/sqrt((3.4)^2/11 + (3.5)^2/10)

                              = 1.193

DF = (s1^2/n1 + s2^2/n2)^2/((s1^2/n1)^2/(n1 - 1) + (s2^2/n2)^2/(n2 - 1))

     = ((3.4)^2/11 + (3.5)^2/10)^2/(((3.4)^2/11)^2/10 + ((3.5)^2/10)^2/9)

     = 19

c) At alpha = 0.01, the critical value is t0.99,19 = 2.539

Since the test statistic value is not greater than the critical value (1.193 < 2.539), so we should not reject the null hypothesis.

No, there is not sufficient evidence to support the claim that student cars are older than faculty cars.


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