Question

You randomly select 22 student cars and find they have a mean age of 8 years and a standard deviation of 3.4 years. You also randomly select 28 faculty cars and find they have a mean age of 5.3 years and a standard deviation of 3.7 years.

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

(a) test statistic
(b) the p-value

Answer 1

The Hypothesis:

H0: =

Ha: >

This is a right tailed test

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Since s₁/s₂ = 3.4/3.7 = 0.91 (it lies between 0.5 and 2) we used the pooled variance.

The degrees of freedom used is n1 + n2 - 2 = 22 + 28 - 2 = 48 (since pooled variance is used)

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The Test Statistic:

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The p Value:    The p value (Right Tail) for t = 2.68 ,df = 48,is; p value = 0.005

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The Decision Rule: If the P value is < , Then Reject H0

The Decision:    Since P value (0.005) is < (0.01), We Reject H0.

The Conclusion: There is sufficient evidence at the 99% significance level to conclude that the students cars are older than faculty cars.