A farmer is concerned that a change in fertilizer to an organic variant might change his crop yield. He subdivides 6 lots and uses the old fertilizer on one half of each lot and the new fertilizer on the other half. The following table shows the results.

Lot ..............Crop Yield Using Old Fertilizer......... Crop Yield Using New Fertilizer

1.......................................... 10................................................ 12

2.......................................... 11................................................ 10

3.......................................... 10................................................ 13

4.......................................... 12................................................. 9

5.......................................... 12................................................ 11

6 ......................................... 11................................................ 12

a. Specify the competing hypotheses to determine whether the median difference between the crop yields differs from zero.

b. At the 5% significance level, what is the decision rule?

c. Calculate the value of the Wilcoxon signed-rank test statistic T.

d. Is there sufficient evidence to conclude that the median difference between the crop yields differs from zero? Should the farmer be concerned? Explain.