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```MAT 214 Lab 11: Decision making
FALL 2008
In this lab we study how to use statistics to make a decision, as well as calculate
the probabilities of making a correct and incorrect decision. We will use Minitab as an
aid in making many decisions and tracking the quality of those decisions.
I.
The problem: Decide whether the mean of a population,  , is greater
than 5 or not greater than 5.
Procedure for making a decision:
 Take a random sample of size 100 and compute X .
 If X  7, decide that the mean of the population,  , is not greater
than 5.
 If X > 7, decide that the mean of the population,  , is greater
than 5.
II.
If Statement
Minitab does not have an “if” statement at the command level, so to
execute an “if” statement we must tell Minitab by using a special file
called a Macro. The file IfStatement.mac contains the instructions
Minitab needs to implement the “if” statement at the command level.
Copy this file to your p: drive. When the following line is put into the
command line editor
%p:\IfStatement.mac 'xBar' 7 'The Decision'
it tells Minitab to make ‘The Decision’ equal 0 if xBar is less than or
equal to 7, and make ‘The Decision’ equal 1 if xBar is greater than 7.
[Technically speaking, Minitab executes the following instruction:
If ‘xBar’  7 then
‘The Decision’ = 0
else
‘The Decision’ = 1
end if
]
Note, a value of ‘Decision’ equal to 1 means we decide  > 5 and a value
of ‘Decision’ equal to 0 means we decided  ≤ 5.
MAT 214 Lab 11: Decision making
III.
FALL 2008
Select a random sample of size 100 from a normal distribution.
Click Start in the lower left hand corner of the screen
Click Programs
Click Accessories
b. Now we’ll type the Minitab commands into Notepad that instruct Minitab
to generate a random sample of size n = 100 from a normal distribution
with mean Mu (we’ll specify Mu later) and standard deviation 12,
compute the sample means, and then execute the if statement (decision
rule). Then it saves ‘The Decision’ in the column named Decisions. Type
Random 100 'Data';
Normal 'Mu', 12.
Let 'xBar' = mean('Data')
%p:\IfStatement.mac 'xBar' 7 'The Decision'
Let 'Decisions' (k1) = 'The Decision'
Let k1 = k1 + 1
c. Let’s let our mean be 5 (i.e ‘Mu’ = 5), and tell Minitab to select 150
random samples of size 100, and for each of the random samples of size
100 execute Decision.txt.
Go to Minitab
Click Edit
Click Command Line Editor
Type the following lines in the Command Line Editor Window
Erase C1, C2
Name C1 'Data'
Name C2 'Decisions'
Name k2 'xBar'
Name k3 'Mu'
Name k4 'The Decision'
Let k1 = 1
Let 'Mu' = 5
Execute "p:\Decision.txt" 150
Click Submit Commands
MAT 214 Lab 11: Decision making
FALL 2008
d. Make a frequency table and determine how many times the decision rule
decided that the mean was ≤ 5 or > 5 (i.e. how many times “The
Decision” was 0 or 1).
Click Stat
Click Tally
Double Click C2 (Decisions)
Click OK
Note the results. Recall the number of 0’s is the number of times the correct
decision was made (i.e. the mean of the population is ≤ 5). Record the proportion of
the samples for which the decision rule decided the mean is ≤ 5 and the proportion of
the samples for which the rule decided the mean is > 5.
Is this what you expected to see?
IV.
Repeat Part III. c and d changing the mean ‘Mu’ to 8. Summarize the results
again as you did above except noting that a right decision is that the mean of
the population is > 5 (i.e. ‘The Decision’ = 1).
V.
Compute the probability X  7 when  is 5 and compare these results with
III. d. Compute the probability X > 7 when  is 8 and compare these results
with IV.
VI.
Repeat Part III. c and d changing the mean  to 7.1. Summarize the results
again as you did above. In this case, the decision rule works as follows:
If X  7, we conclude that  ≤ 5, and if X > 7, we conclude that  > 5.
Comment on the ability of this decision rule to distinguish a mean 7.1 from a
mean of 5.
```
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