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 37 minutes per day. The standard deviation was 13 minutes per day. The mean listening time for a sample of 16 women was also 37 minutes, but the standard deviation of the sample was 14 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?

We reject H0; that there is significant evidence to support that there is difference in the variation in the listening times for men and women

Step-by-step explanation:

Given that :

n1 = 10 ; s1 = 13 ; n2 = 16 ; s2 = 14 ; α = 0.1

Null : H0 : σ1² = σ2²

Alternative : H1 : σ1² ≠ σ2²

To compute the test statistic ; using the Ftest:

F-test = σ2² / σ1² = 14² / 13²

F-test = 14²/13² = 196 / 169 = 1.1597

Decision region :

Reject Null, H0 ; if

Ftest < Fcritical

F critical at:

At α/2 = 0.10/2 = 0.05

df_numerator = 16 - 1 = 15

df_denominator = 10 - 1 = 9

Using F critical calculator :

Fcritical = 3.006

1.1597 < 3.006

Since, Ftest is lesser than Fcritical, then we reject H0

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