Chapter 15.1, Problem 6E

Reconsider the situation described in Exercise 39 of Section 9.3, and use the Wilcoxon test to test the appropriate hypotheses.

39. Scientists and engineers frequently wish to compare two different techniques for measuring or determining the value of a variable. In such situations, interest centers on testing whether the mean difference in measurements is zero. The article “Evaluation of the Deuterium Dilution Technique Against the Test Weighing Procedure for the Determination of Breast Milk Intake” (Amer. J. of Clinical Nutr., 1983: 996–1003) reports the accompanying data on amount of milk ingested by each of 14 randomly selected infants.

	Infant
	1	2	3	4	5
DD method	1509	1418	1561	1556	2169
TO method	1498	1254	1336	1565	2000
Difference	11	164	225	−9	169

	Infant
	6	7	8	9	10
DD method	1760	1098	1198	1479	1281
TO method	1318	1410	1129	1342	1124
Difference	442	−312	69	137	157

	Infant
	11	12	13	14
DD method	1414	1954	2174	2058
TO method	1468	1604	1722	1518
Difference	−54	350	452	540

1. a. Is it plausible that the population distribution of differences is normal?
2. b. Does it appear that the true average difference between intake values measured by the two methods is something other than zero? Determine the P-value of the test, and use it to reach a conclusion at significance level .05.