Posted: June 14th, 2023
SECOND COMPUTER SIMULATION ASSIGNMENT
SECOND COMPUTER SIMULATION ASSIGNMENT: CHAPTER 7 â Sampling
distribution of the mean.
When this assignment is completed
please send it to my graduate assistant (email in Syllabus) via an email
attachment. It will only be accepted in Word (.doc or .docx) format.
That means if you do an assignment using Excel, you must copy and paste the Excel results into Word and save it as .doc
(or .docx and NOT .xls or .xlsx).
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Simulation assignments and random
numbers
Throughout
the term you will be asked to do several simulation assignments. To do those
assignments you must generate random numbers in Excel. For example, using the
Randbetween function.
Each time
Excel calculates the spreadsheet the random numbers change, so it may be
frustrating to generate statistics based on those numbers. For example if you
calculate the mean of the numbers you get a slightly different result each time
you try it.
To avoid this problem I suggest that after you generate the
random numbers the first time, copy them (i.e., highlight them, right click and
choose copy) and then paste them to another part of the spreadsheet by using
the PASTE SPECIAL option. In that option, choose âvaluesâ and then âok.â
If anyone has
a better way of doing this please let me know (for extra credit, of course).
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I made a
video demonstrating this. It can be found in YouTube.
There are 7
parts to this assignment. Please label them in your WORD DOC report (NOT EXCEL
file) to me as Part 1, Part 2, etc.
As before
send them my graduate assistant.
Part
1:
Using
Excelâs Randbetween(0,9) function, generate 200 samples of five random numbers between
0 and 9, calculate the mean of each sample. Show me the list of the 200 means.
Typically, they should look like: 4.8, 3.6, 4.4, 6.0, etc.
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Part
2:
Using
Excel, calculate the overall mean of the 200 sample means (the average of the
averages). This should be around 4.5.
Part
3:
Using Excel,
calculate the standard error of the mean (SEM) (i.e. the standard deviation of the 200 sample
means). We established in the previous simulation that the population average
is 4.5 and the standarddeviation of the
population is 2.87.
Since the SEM= σ.jpg">= σ/√n. The
SEM therefore is 1.28. Thus, the standard deviation of the 200 sample means
should be approximately 1.28.
Part
4:
Using
Excel, make the histogram of the 200 sample means (sampling distribution of the
mean) (use interval size 1, i.e., 0-1, 1-2, 2-3, â¦8-9). According to the
Central Limit Theorem a bell shaped curve should appear. Show me this graph.
Part
5:
Discuss
the intuitive logic of the Central Limit Theorem. Discuss the implications of part
4 in this context. (My videos might help
here.)
Part
6:
Use
2 methods to find P (.gif">>6.3),
(with n=5 as in Parts 1-4): First the z-method of chapter 7 and then by
simply counting how many of your 200 .gif"> were above 6.3.
Part
7:
Discuss
the standard error of the mean. (Explain clearly the reasons why there is an ânâ
in the bottom of the formula; my video might help here as well.)
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Make sure to
label each section Part 1, Part 2 â¦,
Part 7 and only in word.DOC format.
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