Question: Refer to the Journal of Business Logistics (Vol. 36, 2015) study of the factors that lead to successful performance-based logistics projects, Exercise 2.45 (p. 95). Recall that the opinions of a sample of Department of Defense (DOD) employees and suppliers were solicited during interviews. Data on years of experience for the 6 commercial suppliers interviewed and the 11 government employees interviewed are listed in the accompanying table. Assume these samples were randomly and independently selected from the populations of DOD employees and commercial suppliers. Consider the following claim: “On average, commercial suppliers of the DOD have less experience than government employees.”

a. Give the null and alternative hypotheses for testing the claim.

b. An XLSTAT printout giving the test results is shown at the bottom of the page. Find and interpret the p-value of the test user.

c. What assumptions about the data are required for the inference, part b, to be valid? Check these assumptions graphically using the data in the PBL file.

Let ${\mu }_1$be the mean years of experience for commercial suppliers and ${\mu }_2$be the mean years of experience for government employees.

The hypothesis that the company would like to test will be:

Null hypothesis: $H_0:{\mu }_1={\mu }_2$. That is, the mean years of experience for commercial suppliers is not less than the mean years of experience for government employees.

Alternate hypothesis: $H_0:{\mu }_1<{\mu }_2$. That is, the mean years of experience for commercial suppliers are less than the mean years of experience for government employees.

It is given that,

The level of significance 5% is0.05 .

$$\begin{gathered} n_1=6,n_2=11 \\ {\overline{x}}_1=12.33,{\overline{x}}_2=20.82 \\ Z=\frac{\left({\overline{x}}_1-{\overline{x}}_2\right)-\left({\mu }_1-{\mu }_2\right)}{\sqrt{\frac{{{\sigma }_1}^2}{n}+\frac{{{\sigma }_2}^2}{n}}} \\ =\frac{\left(12.33-20.82\right)-0}{\sqrt{\frac{{\left(8.10\right)}^2}{6}+\frac{{\left(8.93\right)}^2}{11}}} \\ =\frac{-8.49}{4.26} \\ =-1.993 \end{gathered}$$

So, the p-value is .046.

As the p-value is less than the significance level, so the null hypothesis will be rejected. Therefore, it can be concluded that the mean years of experience for commercial suppliers is less than the mean years of experience for government employees.

The assumptions are:

• Each sample is taken from simple random sampling.
• Each sample is independent.
• Each sample size is small.
• Each sample is approximately normally distributed.
• The population variance of the two samples is equal.