MIE231 – Tips for Term Project – 2009
The following tips may help you to complete the project. The numbers in square parentheses
indicate the project question number(s) to which the tip may apply.
• [1,4,6,12,13] To generate random numbers, go to Calc Æ Random data. Then, you can select the
distribution that you need and specify the relevant parameters. (Note: The normal distribution
does not have finite endpoints, hence, it is not the correct choice for these questions).
• [2,3] To find probabilities associated with a specified value of a random variable, X, go to Calc
Æ Probability Distributions. Then, select the distribution that you need and specify the
relevant parameters. (Note: you may need to select the Cumulative Probability option. Also, the
column with the specified X-value should be entered in the Input Column field).
•  To calculate a confidence interval (CI) for sample means and standard deviations manually,
use the Z-distribution and χ -distribution equations, respectively.
• [7,8] To find sample means and standard deviations, and the CI for population characteristics,
use the graphical summary (i.e., go to Stat Æ Basic Statistics Æ Graphical Summary).
•  You need to generate two separate graphs: the upper and lower CI limits (CLs) of μ vs.
sample size, and the upper and lower CLs of σ vs. sample size. To plot multiple scatter-plots
on one graph, go to Graph Æ Scatterplot, select the With Connect Line plot type, and click
OK. Next, click on Multiple Graphs and select Overlaid on the same graph under the Multiple
Variables tab. To superimpose reference lines onto the graphs, finish plotting the graphs first,
and then go to Editor Æ Add Æ Reference Lines, and input the required information.
•  The column of 100 data points does not need to be physically separated and un-stacked into
20 separate columns of 5 data points each. Instead, Minitab gives you the option to specify the
subset size when determining control limits (which you will do in Point-11), and then conducts
the “un-stacking” internally. To utilize this option, make sure to enter the subset size in the
Subgroup Size input field when you are in the XBar-S dialog box in Point-11.
•  Control limits can be obtained by creating an XBar-S chart. To do that, go to Stat Æ Control
Charts Æ Variable Charts for Subgroups Æ XBar-S. (Note: The default control limits use
±3 σ. Also, since un-stacking of the data points is unnecessary, you may specify the input data
column to be the same column that contains all your 100 data points).
• [11,14] (μ,σ) values can be set manually by clicking on XBar-S Options in the XBar-S dialog
box, and selecting the Parameters tab to access the Mean and Standard deviation parameter
input fields. When trying to establish the control limits based on a set of sample data (i.e.,
Point-11), no parameters should be specified. Once the process has been established, these
limits should remain the same as new data samples are used on the control chart (i.e., Point-
14). To do that, the unbiased estimators of μ and σ should be entered into the Mean and
Standard deviation input fields, respectively. You will need to use the sample mean and
standard deviation values from Point-11 to calculate these estimators. The unbiased estimator
of μ is the mean of the sample means and the unbiased estimator of σ is the mean of sample
standard deviations/c 4, where c4depends on the size of the data subsets. (Note: The control limits
in Point-14 should remain the same as the ones in Point-11).
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Graphical Summary of a set of data
Summary for n = 100
A nderson-Darling Normality Test
V ariance 1.1937
0 0 N 1
1st Q uartile 9.2420
3rd Quartile 10.7409
8 9 10 11 12