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 men was 31 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 11 women studied was also 31 minutes, but the standard deviation of the sample was 18 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.)

Explanation / Answer

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 F, as alpha =    0.1   ,      
alpha/2 =    0.05          
df1 = n1 - 1 =    9         
df2 = n2 - 1 =    10          
F (crit) =    0.318747439   and   3.020382947  
              
Getting the test statistic, as              
s1 =    11          
s2 =    18          
              
Thus, F = s1^2/s2^2 =    0.37345679          
              
As F is between the two critical values, we FAIL TO REJECT THE NULL HYPOTHESIS.  

Hence, the two tailed P value is also          

P = 0.153919087   

Hence, there is no significant evidence at 0.10 level that there is a difference in the variation in the listening times for men and women. [CONCLUSION]

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