In a sample of 61 business trips taken by employees in the HR department, a comp

Question

In a sample of 61 business trips taken by employees in the HR department, a company finds that the average amount spent for the trips was $1480 with a standard deviation of $450. In a sample of 101 trips taken by the employees in the sales department is $1650 with a standard deviation of $550. When testing the hypothesis (at the 5% level of significance) that the average amount spent on trips taken by the sales department are higher than those taken by the HR department what is the null and alternative hypotheses? (please write out the null and alternative hypotheses below AND on your scratch work...

Explanation / Answer

Let

u1 = mean of HR dept
u2 = mean of sales dept

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    left   tailed test.      
Calculating the means of each group,              
              
X1 =    1480          
X2 =    1650          
              
Calculating the standard deviations of each group,              
              
s1 =    450          
s2 =    550          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    61          
n2 = sample size of group 2 =    101          
Thus, df = n1 + n2 - 2 =    160          
Also, sD =    79.46522281          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    -2.139300615          
              
where uD = hypothesized difference =    0          
              
Now, the critical value for t is              
              
tcrit =    -   1.654432901      
              
              
Also, using p values,              
              
p =    0.016963996          
              
As |t| > 1.654, and P < 0.05, REJECT THE NULL HYPOTHESIS.          

Hence, there is significant evidence that the average amount spent on trips taken by the sales department are higher than those taken by the HR department at 0.05 level. [CONCLUSION]

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Hi! If you use another method/formula in calculating the degrees of freedom in this t-test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!

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