Stat 301 Lab 1 Due January 27, 2014
Use JMP to analyze the data in problem 1 below. It is not sufficient to simply hand in JMP output. You must answer the questions completely. Hand in the JMP output attached at the end of your written (word processed) answers.
1.
A person’s percentage body fat is determined from a person’s density. The density is obtained from the displacement of water in a large tub. A random sample of 44 men below the age of 55 is selected. Each man has his body fat percentage determined from his density.
Go to the course Web site http://www.public.iastate.edu/~wrstephe/stat301.html
Download/open the JMP file that contains the body fat data. a) Summarize the body fat data for the 44 men graphically by creating a histogram and box plot. For the body fat axis have a minimum of 0 and a maximum of 50 with an increment of 10 and no minor ticks. Referring to these graphs, describe the distribution of body fat.
Refer to each graph separately and comment on the shape of the distribution, if there are any possible outliers and describe what in the graph supports your statements. b) Summarize the data numerically and report a five number summary, the sample mean and sample standard deviation for the entire sample of 44 men. c) What does the comparison of the mean to the median tell you about the shape of the distribution of values? d) Report the 95% confidence interval for the population mean body fat. Give an interpretation of this interval and the confidence level. e) The American Council on Exercise (ACE) has a chart that describes different levels of percentage body fat. For male athletes the range of body fat is 6 to 13%. Could this sample be from a population of athletes? Test the hypothesis that the population mean percentage body fat is 13% versus an alternative that the population mean percentage fat is greater than 13%. f) Use JMP to create residuals by subtracting off the sample mean from each of the 44 body fat values. Use Analyze + Distribution to create JMP output that looks at the distribution
(histogram, box plot and Normal Quantile Plot) of the 44 residuals. For the residual axis have a minimum of –30 and a maximum of 30 with an increment of 10 and no minor ticks. g) Refer to the histogram of residuals and indicate what you see and what this tells you about the condition that the random errors are normally distributed. h) Refer to the box plot of residuals. Are there any possible outliers? If so, what are the corresponding body fat values? What does the box plot tell you about the condition of identically distributed random errors? i) Refer to the Normal Quantile Plot of residuals and indicate what you see and what this tells you about the condition that the random errors come from a normal distribution. j) Summarize what you have learned about the conditions necessary for the statistical analysis of body fat percentage from your analysis of the residuals.
2.
On a separate piece of paper write a brief summary of what you have learned about body fat percentages of men under the age of 55.