I. Ertugrul et al. conducted a study to determine the association between insulin growth factor 1 (IGF-1) and bone mineral density (BMD) in men over 65 years of age. The researchers published their results in the paper "Relationship Between Insulin-Like Growth Factor 1 and Bone Mineral Density in Men Aged over 65 Years" (Medical Principles and Practice, Vol. 12, pp. 231-236). Forty-one men over 65 years old were enrolled in the study, as was a control group consisting of 20 younger men, ages 19-62 years. On the WeissStats CD, we provide data on IGF-1 levels (in ng/mL), based on the results of the study. Use the technology of your choice to do the following.
a. Obtain normal probability plots, boxplots, and the standard deviations for the two samples.
b. Based on your results from part (a), which are preferable here, pooled or nonpooled t-procedures? Explain your reasoning.
c. At the 1% significance level, do the data provide sufficient evidence to conclude that, on average, men over 65 have a lower IGF-1 level than younger men?
d. Find and interpret a 99% confidence interval for the difference between the mean IGF-1 levels of men over 65 and younger men.
e. Are your procedures in parts (c) and (d) justified? Explain your answer.