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 10 men was 35 minutes per day. The standard deviation was 10 minutes per day. The mean listening time for a sample of 12 women was also 35 minutes, but the standard deviation of the sample was 12 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

Answer 1

No ;

Explanation:

Given ;

s2 = 10 ; n2 = 10 ; s1 = 12 ; n1 = 12

Hypothesis :

H0 : σ1² = σ2²

H1 : σ1² ≠ σ2²

The test statistic :

Ftest = s1² / s2² = 12² / 10² = 144 / 100 = 1.44

The Pvalue using the Pvalue from Ftest calculator :

Numerator df = 12 - 1 = 11

Denominator df = 10 - 1 = 9

Pvalue = 0.2969

At α = 0.1

If Pvalue > α ; Fail to reject H0

0.2969 > 0.1 ; Hence, we fail to reject the Null

Hence, we cannot conclude that variation exists