MINITAB Assignment 2
(due Friday March 17)
How sample averages approximate the mean
< Text (such as this)
which is enclosed in angle brackets, < >,
is communication about what to do in the assignment,
or commentary about it. I will also color such text
green. Text which is not green and bracketed is
text you should type or paste into the session window,
perhaps with obvious changes, such as replacing
Your Name with your name. This will make your
minitab work more meaningful on review and in execution.
Please try to understand the exercise.>
< In your Minitab reports:
1. You can erase in your session window to get rid
of mistakes and excess. Please do this.
2. Please staple the report you hand in. >
< What you must turn in for this assignment is the
completed session window, together with the annotated
graphs you generate.
(The work below was done at home with the Student Minitab 12 which came
with the text.) >
Part I
The mean of the distribution is the number M such that
the average of a random sample tends to be close to M.
As the sample size gets bigger, the sample average tends to be
closer and closer to M.
In this exercise we use the Minitab data number generator to
see examples of this. The Minitab random data generator produces
samples of numbers which mimic the properties of a specified probability
rule (distribution).
We will use just the Bernoulli (p) Distribution now.
This distribution mimics a coin which is heads ("1") with probability
p and is tails ("0") with probability 1-p. The average/mean for
the distribution is p.
< Get into Minitab, and type into the session window
Your name
Assignment #2: how sample averages approximate the mean >
We generate 25 samples of size 20 of Bernoulli(p) random data
with p=.5, and compute the sample means, as below. (We can think of this
as follows: Minitab takes a crew of 25 people, each crew member
flips a fair coin 20 times, and Minitab writes down his data in a column.)
We apply
Calc > Random Data > Bernoulli , then we
generate 20 rows of data, stored in columns C1-C25.
We apply
Stat > Basic Statistics > Display Descriptive Statistics
< Now erase the rows in your session window which don't have
the mean data, for less clutter (the point of this exercise
is to look at those means, that is, those sample averages).
Notice how the sample averages you see tend to be around .5,
but there is considerable variation. Click
here to see
what resulted in my own session window -- with the randomness, your
numbers will be different. >
< Next, in the data window,
use the mouse to highlight the column titles C1,C2,...,C25
and then hit the backspace key. This should erase the data from those columns.
(This Student Minitab will only handle
5000 data entries in the data window, you
are erasing to clear the way for later operations.) >
Now we repeat the procedure, but with 100 rows instead of 20 rows
(that is, each of the 25 crew members flips 100 times, not just 20
times).
You can click
here to see
what resulted in my own session window. >
Notice that the means we see, from this set of 25 samples, shows less
variation away from .5 then did the previous collection -- this is because
the sample size is bigger.
Finally, we erase the data in the data window columns, and then put the
Bernoulli(.5) sample data for sample size 1000 in the columns C1-C5,
and list out their sample sample averages as before.
We do this three times
(which amounts to looking at 15 samples -- we can't do them
all at once because of that 5000 numbers data limit).
Looking at these 15
samples, you should
see the spread of the sample averages is considerably less
than it was for the smaller sample sizes.
You can click
here
to see
what resulted in my own session window. >
To summarize: for a given probability distribution: the sample average
approximates the mean, and with a bigger sample the approximation is likely
to be better, and with a very big sample the approximation is likely to be very good.
PART II
Erase all the column data in the data worksheet.
In the first three rows of C1, type three numbers of your choice.
Then:
Calc> Calculator
Store result in C2
expression 3 * C1 + 40
Type into your session window your verbal description of what happened.
Then do
Calc > Column Statistics
Pick Mean and input variable C1 .
Then do
Calc > Column Statistics
Pick Mean and input variable C2.
< In my case, I chose in C1 the three numbers 3,4,5 and I got the following:
Column Mean
Mean of C1 = 4.0000
Column Mean
Mean of C2 = 52.000 >
Now, type into your session window an explanation of how you could have
predicted the mean of column 2 just from knowing the mean of column 1 and
the pattern defining column 2.
Print out your session window, to be handed in.
(Be sure your own name is part of the initial page output,
and be sure you have cleaned out
the stuff you don't need.)