Arbitron Media Research Inc conducted a study of the iPod li

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 33 minutes per day. The standard deviation of the sample of the 10 men studied was 11 minutes per day. The mean listening time for the 12 women studied was also 33 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? (Round your answer to 3 decimal places.)

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   sigma1^2 / sigma2^2   =   1  
Ha:    sigma1^2 / sigma2^2   =/   1  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical chi^2, as alpha =    0.1   ,      
alpha/2 =    0.05          
df1 = n1 - 1 =    9         
df2 = n2 - 1 =    11          
F (crit) =    0.322322225   and   2.896222761  
              
Getting the test statistic, as              
s1 =    11          
s2 =    16          
              
Thus, F = s1^2/s2^2 =    0.47265625   [ANSWER, TEST STATISTIC]

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As F is between the two critical values, we DO NOT REJECT THE NULL HYPOTHESIS.              

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Thus, there is no significant difference in the variation in the listening times for men and women. [conclusion]