Reconsider the calorie-burning data in Exercise 10.

Data From Exercise 10

a. Utilize the Wilcoxon signed-rank procedure to test H₀: μ_D = 0 versus H_a: μ_D < 0 for the population of REE differences (IF minus standard diet). What assumption is required here that was not necessary for the sign test?
b. Now apply the paired t test to the hypotheses in part (a). What extra assumptions are required?

c. Compare the results of the three tests (sign, signed-rank, and paired t) and discuss what you find.

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Consider the following data on resting energy expenditure (REE, in calories per day) for eight subjects both while on an intermittent fasting regimen and while on a standard diet ("Intermittent Fasting Does Not Affect Whole-Body Glucose, Lipid, or Protein Metabolism," Amer. J. of Clinical Nutr. 2009: 1244-1251): Diet L.F. Standard Diet L.F. Standard 1 2 1753.7 1604.4 1755.0 1691.1 6 1695.5 1669.7 Subject 3 4 5 1576.5 1279.7 1754.2 1697.1 1477.7 1785.2 Subject 7 1700.1 1901.3 8 1717.0 1735.3 Let μ = true median difference in REE (IF minus standard diet). Test the hypotheses Ho: MD=0 versus Ha: p<0 at the .05 significance level using the sign test.