In the paper ''VoluntaryWeight Reduction in Older Men Increases Hip Bone Loss: The Osteoporotic Fractures in Men Study (Journal of Clinical Endocrinology & Metabolism, Vol. 90, Issue 4, pp. 1998–2004), K. Ensrud et al. reported on the effect of voluntary weight reduction on hip bone loss in older men. In the study, 1342 older men participated in two physical examinations an average of 1.8 years apart. After the second exam, they were categorized into three groups according to their change in weight between exams: weight loss of more than 5%, weight gain of more than 5%, and stable weight (between 5% loss and 5% gain). For purposes of the hip bone density study, other characteristics were compared, one such being body mass index (BMI). On the WeissStats CD, we provide the BMI data for the three groups, based on the results obtained by the researchers.
Use the technology of your choice to do the following tasks.
a. Obtain individual normal probability plots and the standard deviations of the samples.
b. Perform a residual analysis.
c. Use your results from parts (a) and (b) to decide whether conducting a one-way ANOVA test on the data is reasonable. If so, also do parts (d)–(f).
d. Use a one-way ANOVA test to decide, at the 5% significance level, whether the data provide sufficient evidence to conclude that a difference exists among the means of the populations from which the samples were taken.
e. Interpret your results from part (d).