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):

Let μ̃_D = true median difference in REE (IF minus standard diet). Test the hypotheses H₀: μ̃_D = 0 versus H_a: μ̃_D < 0 at the .05 significance level using the sign test.

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Diet 1 2 L.F. 1753.7 1604.4 Standard 1755.0 1691.1 Diet I.F. Standard 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