Question 16.10

16.10 Wheat prices.

Example 7.13 (pages 385-386) reports the results of a small survey that asked separate samples of 5 wheat producers in each of January and July what price they received for wheat sold that month. Here are the data:

wheat

Month Price of wheat ($/bushel)
January $6.6125 $6.4775 $6.3500 $6.7525 $6.7625
July $6.7350 $6.9000 $6.6475 $7.2025 $7.0550

The stemplot on page 386 shows a large difference between months. We cannot assess Normality from such small samples. Carry out by hand the steps in the Wilcoxon rank sum test for comparing prices in January and July.

  1. Arrange the 10 observations in order and assign ranks. There are no ties.
  2. Find the rank sum for July. What are the mean and standard deviation of under the null hypothesis that prices in January and July do not differ systematically?
  3. Standardize to obtain a statistic. Do a Normal probability calculation with the continuity correction to obtain a two-sided -value.