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More statistics (Populations and samples used in research)

Customer Question

the daily travel expenses for the sales staff and the audit staff. She collected the following sample

Sales: 131 135 146 165 136 142
Audit: 130 102 129 143 149 120 139

At the .10 significance level, can she conclude that the mean daily expenses are greater
for the sales staff than the audit staff? What is the p-value?

Submitted: 11 years ago.
Category: Homework
Expert:  Athanassios replied 11 years ago.

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Expert:  Athanassios replied 11 years ago.
My browser does not display the solution correctly. I don't know if this happens for all browsers. Unfortunately I lack the time to rewrite it, as I must be going to work. I hope you can figure the solution out.

Expert:  Athanassios replied 11 years ago.


We have two samples. The mean of the first sample is (131+135+146+165+136+142 ) / 6 = 142.5 

The standard deviation is s1=sqrt((131-142.5)^2 + (135-142.5)^2 + (146-142.5)^2 + (165-142.5)^2 + (136-142.5)^2 + (142-142.5)^2) / (6-1)) = 12.24

Similarly, the mean of the second sample is 130.29 with a standard deviation of 15.79

The test statistic is Z = X1-X2/s

where X1 s the sample mean value for the first sample

X2 is the sample mean value for the second sample

s is the standard deviation of (X1-X2)

s = squareroot(s1^2/n1 + s2^2/n2) =

= sqrt(12.24^2/6+ 15.79^2/7) =

= 7.78

We conduct a right-tailed test , since we only want to check if the mean value of the first population is greater than that of the second population.

At the 0.1 significance level, the critical value is 1.28

Z = X1-X2/s = (142.5-130.29) / 7.78 = 1.569

Since Z = 1.569 exceeds 1.28, we can conclude that the first sample has a greater mean


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