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

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 men was 34 minutes per day. The standard deviation of the sample of the 10 men studied was 13 minutes per day. The mean listening time for the 12 women studied was also 34 minutes, but the standard deviation of the sample was 16 minutes. At the .10 significance level, can we conclude that there is a difference in the variation in the listening times for men and women? (a) Compute the value of the test statistic

Explanation / Answer

Let o1^2 be the variance for men

Let o2^2 be the variance for women

Ho: o1^2=o2^2 (i.e. null hypothesis)

Ha: o1^2 not equal to o2^2 (i.e. alternative hypothesis)

The test statistic is

F=s1^2/s2^2

= 13^2/13^2

=1

It is a two-sided tailed.

Given a=0.1, the critical values are F(0.05, df1=n1-1=10-1=9, df2=n2-1=12-1=11) =0.32 (from F table)

F(0.95, df1=9, df2=11) = 2.896 (from F table)

Since F=1 is between 0.32 and 2.896, 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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