Question

Quarterbacks not only need to have a good passing percentage, but they need to be consistent. That is, the variability in the number of passes completed per game should be small. The table below gives the number of passes completed for Ben Roethlisberger and Aaron Rodgers, quarterbacks for the Pittsburgh Steelers and Green Bay Packers, respectively, during the 2010 NFL season.†

Aaron Rodgers			Ben Roethlisberger
19	21	7		16	20
19	15	25		19	22
34	27	19		17	21
12	22			17	23
27	26			30	22
18	21			18	15

(a) Does the data indicate that there is a difference in the variability in the number of passes completed for the two quarterbacks? Use α = 0.01.

State the null and alternative hypotheses.

H₀: σ₁² = σ₂² versus H_a: σ₁² ≠ σ₂²

H₀: σ₁² ≠ σ₂² versus H_a: σ₁² = σ₂²    

H₀: σ₁² = σ₂² versus H_a: σ₁² < σ₂²

H₀: σ₁² < σ₂² versus H_a: σ₁² > σ₂²

H₀: σ₁² = σ₂² versus H_a: σ₁² > σ₂²

State the test statistic. (Round your answer to two decimal places.)
F =  

State the rejection region. (Round your answer to two decimal places.)
F >  

State the conclusion.

H₀ is not rejected. There is sufficient evidence to indicate a difference in the variability.

H₀ is rejected. There is sufficient evidence to indicate a difference in the variability.    

H₀ is not rejected. There is insufficient evidence to indicate a difference in the variability.

H₀ is rejected. There is insufficient evidence to indicate a difference in the variability.

(b) If you were going to test for a difference in the two population means, would it be appropriate to use the two-sample t-test that assumes equal variances? Explain.

Yes, because the test showed a reason to doubt the equality of the variance assumption.

Yes, because the test did not show any reason to doubt the equality of the variance assumption.    

Yes, because the test did not show any reason to doubt the assumption of normality.

No, because the test did not show any reason to doubt the equality of the variance assumption.No, because the test did not show any reason to doubt the assumption of normality.

Answer 1