Chapter 11.2, Problem 9E

Wilcoxon Signed-Rank Test for n > 30 When you are performing a Wilcoxon signed-rank test and the sample size n is greater than 30, you can use the Standard Normal Table and the formula below to find the test statistic.

$z=\frac{w_s-\frac{n(n+1)}{4}}{\sqrt{\frac{n(n+1)(2n+1)}{24}}}$

In Exercises 9 and 10, perform the Wilcoxon signed-rank test using the test statistic for n > 30.

9. Fuel Additive A petroleum engineer wants to know whether a certain fuel additive improves a car’s gas mileage. To decide, the engineer records the gas mileages (in miles per gallon) of 33 randomly selected cars with and without the fuel additive. The table shows the results. At a = 0.10, can the engineer conclude that the gas mileage is improved?