Question

Arbitron Media Research Inc. conducted a study of the iPod listening habits of men and women. One facet of the study involved the mean listening time. It was discovered that the mean listening time for a sample of 9 men was 33 minutes per day. The standard deviation was 7 minutes per day. The mean listening time for a sample of 21 women was also 33 minutes, but the standard deviation of the sample was 18 minutes. At the 0.10 significance level, can we conclude that there is a difference in the variation in the listening times for men and women? (Round your answer to 3 decimal places.)

a. The test statistic is _____

b. The decision: ______

Answer 1

The statistical software output for this problem is:

Two sample variance summary hypothesis test:

σ₁² : Variance of population 1
σ₂² : Variance of population 2
σ₁²/σ₂² : Ratio of two variances
H₀ : σ₁²/σ₂² = 1
H_A : σ₁²/σ₂² ≠ 1

Hypothesis test results:

Ratio	Num. DF	Den. DF	Sample Ratio	F-Stat	P-value
σ12/σ22	8	20	0.15123457	0.15123457	0.01

Hence,

a) Test statistic = 0.151

b) The decision: Reject Ho. There is sufficient evidence to conclude a significant difference between the variations in the listening time of men and women.