Arbitron Media Research Inc. conducted a study of the iPod listening habits of m

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 42 minutes per day. The standard deviation was 16 minutes per day. The mean listening time for a sample of 13 women was also 42 minutes, but the standard deviation of the sample was 15 minutes. At the 0.02 significance level, can we conclude that there is a difference in the variation in the listening times for men and women

test statistics-

decision-

Explanation / Answer

Hypothesis

Ho: variance(men)=Variance(women)

H1: variance(men)!=Variance(women)

TEst Statistics:

F =(15)^2/(16)^2 = 0.8789

Critical value:

It is a two-sided tailed.

Given a=0.02, the critical values are F(0.02, df1=n1-1=10-1=9, df2=n2-1=13-1=12) =0.24 from f table

F(0.98, df1=9, df2=12) = 3.66 (from F table)

Since F=0.8789 is between 0.32 and 3.66, we do not reject Ho.

So we can not conclude that there is a difference in the variation in the listening times for men and women

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