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In: Statistics and Probability

In a sample of 58 business trips taken by employees in the HR department, a company...

In a sample of 58 business trips taken by employees in the HR department, a company finds that the average amount spent for the trips was $1,462 with a standard deviation of $440. In a sample of 86 trips taken by the employees in the sales department is $1,688 with a standard deviation of $569. When testing the hypothesis (at the 5% level of significance) that the averageamount spent on trips taken by the sales department are higher than those taken by the HR department what is the test statistic? (please round your answer to 2 decimal places)

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Expert Solution

Sample #1   ----> HR
mean of sample 1,    x̅1=   1462.00          
standard deviation of sample 1,   s1 =    440          
size of sample 1,    n1=   58          
                  
Sample #2   ----> Sales   
mean of sample 2,    x̅2=   1688.000          
standard deviation of sample 2,   s2 =    569.00          
size of sample 2,    n2=   86          
                  
difference in sample means = x̅1-x̅2 =    1462.000   -   1688.0000   =   -226.0000
                  
std error , SE =    √(s1²/n1+s2²/n2) =    84.2769          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   -226.0000   /   84.2769   ) =   -2.68

orchestra answered 1 year ago
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