Math 117 Computer Lab
Assignment – Sampling Distributions
(Due at the beginning of lab
next week – 3/1 or 3/3)
For this
assignment, you will do a sampling distribution simulation similar to what we
did in lab with the uniform distribution, but you will work with the exponential distribution. Be sure to start early and ask if you have
any Minitab questions. Also, Minitab graphs can easily be copied, pasted, and
resized in Word, so you can fit two
graphs on the same page.
- Have
Minitab randomly draw 1000 values from the exponential (not uniform) distribution (Calc>Random
Data>Exponential; keep Minitab’s default values of “Scale” and “Threshhold”). The distribution of these 1000 values
gives a good estimate of what the exponential distribution looks like.
Create a histogram of these 1000 random draws from the exponential
distribution (and turn this graph in).
How would you describe the shape of this distribution?
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- Now
randomly generate 1000 rows from the exponential distribution and store
them in columns 2 through 51. Think of these data as 1000 samples, each of
size 50, from the exponential distribution. Via Calc>Row Statistics,
create a column that contains the sample means for these 1000 samples.
Create a histogram of these 1000 sample means (and turn this graph in). How would you describe the shape of
the distribution of sample means?
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- The
particular exponential distribution you are working with has mean 1 and
standard deviation 1. That is, for this population, the mean,
, is 1 and the standard deviation, 
, is 1. Then, theoretically, what
are the mean and standard deviation of the sampling distribution of the
sample mean (based on samples of size
50)? (That is, find 
and 
, based on the formulas provided in
the textbook and discussed in class.)
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- Your
column of 1000 sample means is an estimate of the sampling distribution of
the sample mean. Determine the mean and standard deviation for your column
of means (Stat>Basic Statistics>Display Descriptive Statistics) and
write these values below. Are these values close to the theoretical values
you found in part 3?
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- How does
this entire exercise (particularly
part 2) illustrate the Central Limit Theorem?
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