The National Association of Home Builders provided data on t

The National Association of Home Builders provided data on the cost of the most popular home remodeling projects. Sample data on cost in thousands of dollars for two types of remodeling projects are as follows.

Test statistic for the difference in the two means

Kitchen 25.2 17.4 22.8 21.9 19.7 Master Bedroom 18.0 22.9 26.4 24.8 26.9 Kitchen 23.0 19.7 16.9 21.8 23.6 Master Bedroom 17.8 24.6 21.0

Solution

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 =    21.2          
X2 =    22.8          
              
Calculating the standard deviations of each group,              
              
s1 =    2.70472837          
s2 =    3.551659572          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    10          
n2 = sample size of group 2 =    8          
Thus, df = n1 + n2 - 2 =    16          
Also, sD =    1.519322635          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    -1.053100877   [ANSWER]

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Additional info:      
              
where uD = hypothesized difference =    0          
              
Now, the critical value for t is              
              
tcrit =    +/-   2.119905299      
              
Thus, comparing t and tcrit, we decide to   WE FAIL TO REJECT THE NULL HYPOTHESIS.          
              
Also, using p values,              
              
p =    0.307939618          
              
Comparing this to the significance level,    WE FAIL TO REJECT THE NULL HYPOTHESIS.