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.

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 significance level .05.

Infant DD method 1509 1418 156 1556 2169 TW method 1498 1254 1336 1565 2000 Difference 11 64 225 9 169 Infant 10 DD method 1760 1098 1198 1479 1281 TW method 1318 1410 1129 1342 1124 69 137 157 Difference 442-312 Infant 12 13 14 DD method TW method Difference 1414 1468 54 1954 1604 350 2174 1722 452 2058 1518 540