Almost two-thirds of iron in the body is found in hemoglobin, the protein in the red blood cells that carries oxygen to the tissues. Iron deficiency could lead to anemia, a condition characterized by less than the normal quantity of hemoglobin in the blood. The following data gives the hemoglobin values for 7 female patients at risk for anemia, before and after they followed a 3-month dietary iron intake program: Before After 11.4 12.3 12.5 13.6 10.6 13.7 9.7 10.3 12.5 14.3 12.8 13.9 11.7 12.8

a) Was the program efficient in increasing the hemogloblin level? Justify your answer using a test of hypothesis for H0: mu1= mu2 against H1: mu1< mu2 , where mu1 and mu2 are the average hemoglobin levels before and after the program, respectively. Use the level alpha=0.01

b) What is the conclusion of a test of level alpha=0.01, if we assume (incorreclty) that the hemoglobin level after the program is independent of the hemoglobin level before the program? Assume that the two populations are normally distributed with equal variances.