Data on household vehicle miles of travel VMT are compiled a

Data on household vehicle miles of travel (VMT) are compiled annually by the Federal Highway Administration and are published in National Household Travel Surve, Summary of Travel Trends. Independent random samples of 15 Midwestern households and 14 southern household provided the following data on last year\'s VMT, in thousands of miles:

Solution

1.

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   =   0  
Ha:   u1 - u2   =/   0  
At level of significance =    0.05          
As we can see, this is a    two   tailed test.      
Calculating the means of each group,              
              
X1 =    16.23          
X2 =    17.69          
              
Calculating the standard deviations of each group,              
              
s1 =    4.06          
s2 =    4.42          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    15          
n2 = sample size of group 2 =    14          
Thus, df = n1 + n2 - 2 =    27          
Also, sD =    1.579355504          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    -0.924427715          
              
where uD = hypothesized difference =    0          
              
Now, the critical value for t is              
              
tcrit =    +/-   2.051830516      
              
As |t| < 2.0518, WE FAIL TO REJECT THE NULL HYPOTHESIS.  

Thus, there is no significant evidence that there is a difference in last year\'s mean VMT for Midwestern and Southern households. [CONCLUSION]