Are these trips equal in terms of monetary revenue Test at

Are these trips equal in terms of monetary revenue? Test at = .01 significance level. MountainDew: Average daily revenue = $1000.00; standard deviation = 20.0; n = 11 NewHorizon: Average daily revenue = $1150.00; standard deviation = 80.0; n = 13

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   =   0  
Ha:   u1 - u2   =/   0  
At level of significance =    0.01          
As we can see, this is a    two   tailed test.      
Calculating the means of each group,              
              
X1 =    1000          
X2 =    1150          
              
Calculating the standard deviations of each group,              
              
s1 =    20          
s2 =    80          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    11          
n2 = sample size of group 2 =    13          
Thus, df = n1 + n2 - 2 =    22          
Also, sD =    22.99285386          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    -6.523766076          
              
where uD = hypothesized difference =    0          
              
Now, the critical value for t is              
              
tcrit =    +/-   2.818756061      
              
Also, using p values,              
              
p =    1.46026E-06          
              
As |t| > 2.8187, and P < 0.01,    WE REJECT THE NULL HYPOTHESIS.          

Thus, there is significant difference in the mean daily revenues for these trips at 0.01 level. [CONCLUSION]

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