In the sample of 23 young adult men, the correlation between the total hemoglobin (THb) measured from the venipuncture and measured from the finger needle puncture was 0.82. For a sample of 32 women of similar age, the correlation was 0.74. The two samples from each and every person were collected in one hour of each other. Suppose that the straight-line regression assumptions hold.
a. Test the hypothesis that the two population correlations are same. Employ a two-tailed test. What do you conclude?
b. If the experimenter had planned to do so before collecting data, a valid one-tailed test could have been conducted. With this assumption, repeat part(a) but employ a one-tailed test to measure whether the correlation for women is lower than that for men. What do you conclude?
c. Suppose that the researcher had planned to conduct the one-tailed test of hypothesis that the correlation for women is higher than that for men. What test must be conducted? What do you conclude.