Introductory Lab Activities
Activity 4: Graphically Assessing Normality
Data Set: Fitness.jmp
Summary
Mr. Teaque runs the World Fitness Class Gym, which has more than 500 members. Members of this gym must be older than 35 but younger than 60. He has selected a random sample of members and collected data on their running time and pulse rate. Before any statistical analysis can be completed, he must make sure the data can be regarded as a sample from a normal population.
In this lab you will use a JMP data set called Fitness. You will investigate whether the data are normal using the 68-95-99.7 rule and the normality quantile plot. Use this document as a worksheet.
The Fitness Data
Open the file Fitness.jmp (go to Help > Sample Data, then click See an Alphabetical
List of all Sample Data Files).
The data table has nine columns and 31 rows. The columns represent the name, sex, age, weight, oxygen consumption (Oxy), runtime, running pulse, resting pulse and maximum pulse for the particular subjects.
The question of interest is whether the values in each column are distributed in such a way that they are modeled well by a normal distribution.
Investigating Normality Using the 68-95-99.7 Rule
You will need to find out how many data points fall within one, two and three standard deviations above and below the mean. You will explore two ways of finding this
information:
Method 1: Stem and leaf plot (when you have small data sets)
Method 2: Data sorting (when you have larger data sets)
Method 1 – Stem and Leaf Plot
From the Distribution output window for Weight, select Stem and Leaf from the red triangle next to Weight.
What can you see on the stem and leaf plot that you could not see on the histogram (answer in complete sentences)?
In this data set what percent does each data point contribute?
Using the 68-95-99.7 rule, how many data points, for this particular set, would need to be included within one standard deviation above and below the mean to cover 68% of
the data?
Calculate the mean plus and minus one standard deviation (the interval that should include 68% of the data)
What percent of your data is in that interval?
Calculate the mean plus and minus two standard deviations (the interval that should include 95% of the data).
What percent of your data is in that interval?
Calculate the mean plus and minus three standard deviations (the interval that should include 99.7% of the data).
What percent of your data is in that interval?
From this information, would you conclude that the population distribution appears to be approximately normal? Explain (again, answer in complete sentences)
On the normal quantile plot, what variables do the axes represent?
Horizontal:
Vertical:
Does the normal quantile plot support the assumption that the population distribution is approximately normal? Justify your answer (answer in complete sentences).
Homework
Investigate the normality of the running time (Runtime) and resting pulse (RstPulse) data.
Justify your answer using the 68-95-99.7 rule and the normal quantile plot.
Include statistical justification and specific numerical values.
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