A corporate analyst is testing whether mean inventory turnover has increased. Inventory turnover in six randomly chosen product distribution centers (PDCs) is shown. $\begin{array} { |l | c | c | }
\hline & { \text { This Year } } & \text { Last Year } \
\hline \text { PDC 1 } & 5.1 & 4.1 \
\hline \text { PDC 2 } & 3.9 & 2.9 \
\hline \text { PDC 3 } & 4.8 & 2.8 \
\hline \text { PDC 4 } & 3.4 & 3.4 \
\hline \text { PDC 5 } & 4.6 & 2.6 \
\hline \text { PDC 6 } & 7.7 & 4.7 \
\hline
\end{array}$ The value of the test statistic is:
A)3.798
B)2.449
C)1.225
D)3.503

Question

A corporate analyst is testing whether mean inventory turnover has increased. Inventory turnover in six randomly chosen product distribution centers (PDCs) is shown. $\begin{array} {  |l | c | c | } 
\hline & { \text { This Year } } & \text { Last Year } \
\hline  \text { PDC 1 } & 5.1 & 4.1 \
\hline  \text { PDC 2 } & 3.9 & 2.9 \
\hline  \text { PDC 3 } & 4.8 & 2.8 \
\hline \text { PDC 4 } & 3.4 & 3.4 \
\hline  \text { PDC 5 } & 4.6 & 2.6 \
\hline  \text { PDC 6 } & 7.7 & 4.7 \
\hline
\end{array}$ The value of the test statistic is:
A)3.798
B)2.449
C)1.225
D)3.503

Quizplus · Accepted Answer

We need to perform a paired t-test since we are comparing means from the same distribution centers from two different years. 
The null hypothesis is that there is no difference in mean inventory turnover between this year and last year, and the alternative hypothesis is that mean inventory turnover has increased this year.

Using a calculator, we find that the paired t-test statistic is 3.503.

We can compare this with the t-distribution table (with 5 degrees of freedom, since we have 6 pairs of data), and find that at alpha = 0.05, the critical value is 2.571. Since our test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is evidence to suggest mean inventory turnover has increased this year.

A Corporate Analyst Is Testing Whether Mean Inventory Turnover Has