Ages of Stowaways The Queen Mary sailed between England and

Ages of Stowaways The Queen Mary sailed between England and the United States, and stowaways were sometimes found on board. The ages (in years) of stowaways from eastbound crossing and westbound crossings are given below (data from the Cunard Steamship Co., Ltd.). Compare the variation in the two data sets. Eastbound: 24 24 34 15 19 22 18 20 20 17 Westbound: 41 24 32 26 39 45 24 21 22 21

Solution

Getting the standard deviations of the two sets,

s(east) = s1 = 5.313504807  
s(west) = s2 = 9.019115502

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 =    0.05   ,      
alpha/2 =    0.025          
df1 = n1 - 1 =    9         
df2 = n2 - 1 =    9          
F (crit) =    0.248385855   and   4.025994158  
              
Getting the test statistic, as              
s1 =    5.313504807          
s2 =    9.019115502          
              
Thus, F = s1^2/s2^2 =    0.347083732          
              
As F is between the two critical values, we FAIL TO REJECT THE NULL HYPOTHESIS.              

Thus, there is no significant evidence that the variances of the two groups are not equal. [CONCLUSION]

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Hi! I used the F test for variances to determine if the variances are equal.

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