Stat 301
Lab 1
Due September 8, 2014
1. A child’s height is affected by many factors. For this assignment you will look at data on the
heights (in inches) of 100 randomly selected children between the ages of 3 and 19 years old.
The purpose of this assignment is to describe the sample of children’s heights, make
inferences to the population from which the children were selected and to check the
conditions necessary to make those inferences. You should use JMP to create plots of the
sample data, summarize the sample data and make inferences from the sample to the
population. You should also use JMP to aid in the checking of the conditions necessary for
inference. JMP is a computing tool that does the number crunching for you. You still have
to answer the questions posed below. Turn in the answers to the questions below and attach
your JMP output at the end of the assignment. You can download/open the JMP file that
contains the height data from the course Web site
http://www.public.iastate.edu/~wrstephe/stat301.html
a) Summarize the heights for the sample of 100 children graphically by creating a histogram
and box plot. For the height axis have a minimum of 40 and a maximum of 80 with an
increment of 5 and no minor ticks. Referring to these graphs, describe the distribution of
height. 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 sample height data numerically by reporting a five number summary, the
sample Interquartile Range (IQR), the sample mean and sample standard deviation for the
entire sample of 100 children.
c) Are the values of the sample mean and sample median consistent with the shape of the
distribution you describe in a)? Explain briefly.
d) Report the 95% confidence interval for the population mean height. Give an
interpretation of this interval and the confidence level.
e) Test the hypothesis that the population mean height is 60 inches versus an alternative that
the population mean height is greater than 60 inches.
f) Use JMP to create residuals by subtracting off the sample mean from each of the 100
heights. Use Analyze + Distribution to create JMP output that looks at the distribution
(histogram, box plot and Normal Quantile Plot) of the 100 residuals. For the residual axis
have a minimum of –20 and a maximum of 20 with an increment of 5 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 heights? 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 height from your analysis of the residuals.
2. On a separate piece of paper (this sheet will be graded separately from your answers to part 1)
write a brief summary of what you have learned about height of children between the ages of
3 and 19.