42. 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. Clin. Nutrit., 1983:

996—1003) reports the accompanying data on measuring amount of milk ingested by each of 14 randomly selected infants.

a. Is it plausible that the population distribution of differences is normal?

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 signi cance level .05.

c. What happens if the two-sample t test is (incorrectly)

used? Hint: s1  352.970, s2  234.042 Infant Method 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Isotopic 1509 1418 1561 1556 2169 1760 1098 1198 1479 1281 1414 1954 2174 2058 Test 1498 1254 1336 1565 2000 1318 1410 1129 1342 1124 1468 1604 1722 1518 Difference 11 164 225 9 169 442 312 69 137 157 54 350 452 540