Researchers measured blood levels of the hormone Androstenedione (Andro) in each of 24 women. Among 12 women who had recently fallen in love, the sample mean was 2.1 ng/ml; the SD of these data was 0.7. Among 12 women who had not recently fallen in love, the mean was 1.9, and the SD was 0.7. Formula (6.7.1) yields 22 degrees of freedom.
(a) Conduct a two-sample t test, with non directional alternative; show all steps, including bounds on the P-value. If α = 0.05, do you reject H0? Why or why not?
(b) A 90% confidence interval for the difference in mean Andro levels for the two populations is (-0.39,0.79) ng/ml. Suppose a change of 0.4 ng/ml is medically important. Are these results medically important? Briefly explain your reasoning.