Ms. Lisa Monin is the budget director for Nexus Media.She would like to compare

Question

Ms. Lisa Monin is the budget director for Nexus Media.She would like to compare the daily travel expenses for the sales staff and the audit staff.She collected the following sample information:

Sales ($)          141      135      146      165      136      142

Audit ($)         130      102      129      143      149      120      139

A) Can we conclude that the variation in audit and sales expenses is the same?

B) At the .05 significance level, can we conclude that the mean daily expenses are greater for the sales staff than for the audit staff?

C) What is the p-value? How would you explain it to your boss?

(Please post steps on how you got to each answer)

Explanation / Answer

a)

Let group 1 = sales group
group 2 = audit group

Getting their standard deviations,

s1 = 10.98028536  
s2 = 15.78727637

Thus, we cannot conclude that the variation are the same.

b)

We don't pool the data because their standard deviations are not close.

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    right   tailed test.      
Calculating the means of each group,              
              
X1 =    144.1666667          
X2 =    130.2857143          
              
Calculating the standard deviations of each group,              
              
s1 =    10.98028536          
s2 =    15.78727637          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    6          
n2 = sample size of group 2 =    7          
Thus, df = n1 + n2 - 2 =    11          
Also, sD =    7.463235667          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    1.859910768          
              
where uD = hypothesized difference =    0          
              
Now, the critical value for t is              
              
tcrit =    +   1.795884819      
              
Thus, comparing t > tcrit, we decide to   WE REJECT THE NULL HYPOTHESIS.          
      
Thus, there is significant evidence at 0.05 level that the mean daily expenses are greater for the sales staff than for the audit staff. [CONCLUSION]

********************

C)
      
Also, using p values,              

As, df = 11, using technology,
              
p =    0.04491383          
              
              
Hence, there is only 4.49% chance that this result only happened by chance, which is small. Thus, it is reasonable to believe that the the mean daily expenses are greater for the sales staff than for the audit staff.

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