a. Exercise 2—Wilcoxon-Signed Rank Test

The 1997 price/earnings ratios for a sample of 12 stocks are shown in the following list ( Barron’s, December 8, 1997). Assume that a financial analyst has provided the estimated price/earnings ratio for 1998. Using a .05 level of significance, what is your conclusion about the differences between the price/earnings ratios for 1997 and 1998?

Solution Exercise b.

Now we use Wilcoxon-Signed Rank Test. First, we have to make a table with the difference between the two years 1997 and 1998

Now we build the following rank table:

This way the statistics is S = 72.5, and also

and

Using these quantities, we define:

(the “-1/2” comes from continuity correction). For the given significance, we reject the

null hypothesis if Z>R, where R=1.644853 at the 0.05 level of significance. Therefore, we conclude that there’s a difference (decrease) between the 1997 P/E and the 1998 P/E.