J. McWhorter et al. of the College of Health Sciences at the University of Nevada, Las Vegas, studied physical therapy students during their graduate-school years. The researchers were interested in the fact that, although graduate physical-therapy students are taught the principles of fitness, some have difficulty finding the time to implement those principles. In the study, published as “An Evaluation of Physical Fitness Parameters for Graduate Students” a sample of 27 female graduate physical therapy students had a mean of 22.46 percent body fat.

a. Assuming that the percent body fat of female graduate physical therapy students is normally distributed with standard deviation 4.10 percent body fat, determine a 95% confidence interval for the mean percent body fat of all female graduate physical therapy students.

b. Obtain the margin of error, E, for the confidence interval you found in part (a).

c. Explain the meaning of E in this context in terms of the accuracy of the estimate.

d. Determine the sample size required to have a margin of error of 1.55 percent body fat with a 99% confidence level.