In order to determine whether or not there is a significant

In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated.

What is the p-value for this hypothesis test?

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 =    10.8          
X2 =    10          
              
Calculating the standard deviations of each group,              
              
s1 =    2          
s2 =    1.5          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    80          
n2 = sample size of group 2 =    60          
Thus, df = n1 + n2 - 2 =    138          
Also, sD =    0.295803989          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    2.704493615          
              
where uD = hypothesized difference =    0          
              
              
Thus, using p values,              
              
p =    0.007   [ANSWER, OPTION B]