In a sample of 23 young adult men, the correlation between total hemoglobin (THb) measured from venipuncture and measured from a 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 person were collected within 1 hour of each other. Assume that the straight-line regression assumptions hold.
a. Test the hypothesis that the two population correlations are equal. Use a two-tailed test. What do you conclude?
b. If the experimenter had planned to do so before collecting the data, a valid one-tailed test could have been conducted. With this assumption, repeat part (a), but use a one-tailed test to assess whether the correlation for women is lower than that for men. What do you conclude?
c. Assume that the researcher had planned to conduct a one-tailed test of the hypothesis that the correlation for women is higher than that for men. What test should be conducted? What do you conclude?