 # statistical modelling

statistical modelling
Stage 3 of the statistical modelling assignment instructions , This section is 8%, the other 2%sections will be moodle quizzes you can try as many times as you want before the final.

You need to submit a word file to turnitin discussing the uses and abuses of statistics, the turnitin match can be high because quantitative methods has many common phrases that everyone uses without a citiation however be aware if it is clear that you are just cut and pasting from other students then that is academic misconduct.
You will need to cut and paste suitable diagrams from Microsoft excel into a single word document to support your arguments
It is reccommentded that final version is saved as a word 1997-2003 document because otherwise you have to make sure your document does not have links to excel files,

If you are not saving as a word 1997-2003 document be careful when you paste charts from excel paste them as images, so paste by right clicking and selecting image
this will probably be the icon with a picture of a mountain, Avoid any options with links and/or a chain, You MUST not
link the excel file to the word document you submit to turnitin because you are only submitting the word document to turnitin. If pictures are actually linked you can unlink them at any stage.

The assignment has 4 sections ,
Section 1 instructions
Paste in the relevant tables from assignment stage 1 question 9 and 10 and discuss them, if you did not get marks for these when you did the assignment you will get full marks if you discuss them properly in stage
Section 2 instructions
Paste in two examples of ANOVA , (use http://statpages.org/anova1sm.html)
and two examples of the Chi square test of independence (use http://www.quantpsy.org/chisq/chisq.htm )
And use these to explain roughly what a p-value is, If the lecturer thinks your explanation would help students roughly understand what a p-value is then you will get high marks.
Section 3 instructions
need to discuss the results in the use the excel file“1000 sample means of gambling game A and B” using the guide on pages 2 to 5 of this document.
Section 4 insttructions
Discuss the uses and abuses of statistics , you have 2 options, you only need to do one
option 1 give a brief summary of http://news.bbc.co.uk/1/hi/magazine/7542886.stm

option 2 is more abstract so you if you pick this option you can resubmit it if you make a legimate attempt
The typical bus701 student is too busy paying the bills to make a legitimate attempt to learn the material
Option 2 needs you to provide examples about why Hypothesis testing is is hard to learn or hard to teach.
Refer to the last page of the instructions
Instructions for for section 3 page 1 of 4
You have to discuss the excel file “1000 sample means of gambling game A and B”
1) open the file “1000 sample means of gambling game A and gambling game B”
It is simpler than real life
Assume that every day there is a casino where there are 100 plays of gambling machine A and there are 100 plays of gambling machine B and the averages for the last 1000 days have been recorded.

Cut and paste the distribution of a gambling game (refered to it as gambling machine A) into a word document

Click the “percentile 1000 sample means A” tab

And cut and paste the plot of percentiles with percentile on the y axis and sample average on the x axis and mark the 5th , 25th, 50th and 75th and 95th percentile on the plot Also type down the 5th , 25th, 50th and 75th and 95th percentile of the average of 100 plays (you can just give rough estimates using the chart

2) Verify the mean µ and standard error of the average of 100 plays by calculating all the values by hand.
(Either cut and paste from lecture notes and change the numbers or do it by hand and take a photo an include the photo in the word document)
Instructions for for section 3 page 2 of 4
3) Click the mean of gambling machine B tab

For gambling machine B YOU MUST MAKE UP YOUR OWN numbers, The only rules are that the total probability is 1 and each probability is between 0 and 1
4)
Click the percentile of 1000 means of B tab

cut and paste a plot with percentile on the y axis and sample average on the x axis and mark the 5th , 25th, 50th and 75th and 95th percentile on the plot Also type down the 5th , 25th, 50th and 75th and 95th percentile of the average of 100 plays (you can just give rough estimates using the chart

5) Verify the mean µ and standard error of the average of 100 plays of gambling machine B by calculating all the values by hand.
(Either cut and paste from lecture notes and change the numbers or do it by hand and take a photo an include the photo in the word document)

6) Briefly explain why the information 1 to 4 would be useful for a casino Manager, Compare and Contrast gambling machine A to gambling machine B
300 words is more than enough

Instructions for for section 3 page 3 of 4
7) Click on the scatter plot of the average of gambling machine A against the average of Gambling machine B

Attach a scatter plot of gambling machine A an Gambling Machine B
is the correlation close to -1 , close to 0 or close to 1?

8) Click on the “total A+B and total A-B” tab
Paste in the diagram and comment (your comment should demonstrate you have read and understood lecture notes about quantitative methods)
Instructions for for section 3 page 4 of 4

9) Click on the “z score vs finding z from chart” tab , It is for gambling machine A, But the same thing happens for
gambling machine B , and A-B and A+B
10) Paste in the chart into your assignment note that you will have to comment on the regression line and
the correlation r so you will have to look at the fitted line

Understand that this a plot with 1000 points based on gambling machine A
On the x-axis is the z score of game for each day,
the formula is
Z-score =(average for one day- average of all 1000 daily averages)/ standard deviation of 1000 averages

On the y-axis is the z from percentile for each day
Each daily average has a percentile and you can use the percentile to find a Z value using the
z chart

a) if the slope is close to 1 and if the intercept is close to 0
What is the relationship between the
zscore
and
z from percentile ?

b) pick any 2 days with percentiles between 0.25 and 0.75 and verify
the z-score and z from by percentile by hand and mark both of these points on the chart.

c) Is the correlation coefficient r close to -1 , 0 or 1?

d) Is the slope actually close to 0 and the intercept close to 1
e) Give a brief comment of what the scatterplot shows you, your answer should demonstrate you have read and understood th lecture notes about quantitative methods

Instructions for section 4
There are two options you have to do one option
Option 1
give a brief summary of
http://news.bbc.co.uk/1/hi/magazine/7542886.stm

Just 300 words is enough
Opition 2
Discuss why hypothesis testing is hard to learn and hard to teach
As an example you can
Give a brief discussion of why the information of question 8,9 and 10 are abstract and counter intuitive ,
and you can give details your struggles to understand hypothesis testing, It is ok if you only partly understand it, to fully understand hypothesis testing you need to fuly understand why the following 3 different things can be treated as the same thing when you have a large list of
estimates and the null hypothesis is true
1)z score = (Estimate – mean of list of estimates)/(standard deviation of the list of estimates)
2) Z found by looking up the estimates percentile on the z chart, The estimates percentile is found by comparing the estimate to all of the other estimates
3) z-test stat = (Estimate- claimed value)/standard error “
Finally give a discussion of hypothesis testing in rough terms and how a typical person should learn about hypothesis testing.

Appendix, this is not the assignment but it will help you understand the assignment
Here is a sample final exam multiple choice question that is related to the discussion make about the differences between gambling machine A and gambling Machine B

1)
Suppose a casino has two gambling games and for simplicities sake each game is played 100 times each day ,
the results of 1000 days have been recorded.
In the following scatterplot For the scatterplot
On the Y axis is the sample mean of gambling machine A on a specific day
On the Xaxis is the sample mean of gambling machine B on a specific day

The percentile plot of mean of A+ mean of B and mean of A- mean of B is given below

Which of the following facts does the information above demonstrate if A and B are independent
A) Standard deviation of (A+B)= standard deviation of (A-B)
B) Correlation between A and B is 0
C) Both (A) and (B) are correct
D) None of the options are correct
Answer is C) A+B and A-B seem to have the same spread , if spread is the same then standard deviation is the same , since variance is standard deviation squared then the variance is the same ,
There is no clear relationship in the scatterplot so the correlation is 0

This is not in the assignment This is a sample final exam question that will help you understand the assignment

Consider the following sample of 3 days were temperature and sales of cold drinks are recorded
day X= Temperature Y= Sales Z of temperature Z of sales
1 0 3 -1
2 1 5 0
3 2 7

.a) What is the intercept
.b) What is the slope
.c) Fill in the missing z scores, note that
X has a mean of 1 and standard deviation of 1
Y has a mean of 5 and standard deviation of 2
.d) What is the coefficient of correlation r
Solution
Solution
.a) 3
.b) 2
.c)
day X= Temperature Y= Sales Z of temperature Z of sales
1 0 3 (0-1)/1=-1 (3-5)/2=-1
2 1 5 (1-1)/1=0 (5-5)/2=0
3 2 7 (2-1)/1=1 (7-5)/2=1
.d) r=1

This is not in the assignment This is a sample final exam question that will help you understand the assignment

Consider the following sample of 3 days were temperature and sales of hot drinks are recorded
day X= Temperature Y= Sales Z of temperature Z of sales
1 0 10
2 1 8
3 2 6

.a) What is the intercept
.b) What is the slope
.c) Fill in the missing z scores, note that
X has a mean of 1 and standard deviation of 1
Y has a mean of 8 and standard deviation of 2
.d) What is the coefficient of correlation r
Solution
.a) 10
.b) -2
.c)
day X= Temperature Y= Sales Z of temperature Z of sales
1 0 10 (0-1)/1=-1 (10-8)/2=1
2 1 8 (1-1)/1=0 (8-8)/2=0
3 2 6 (2-1)/1=1 (6-8)/2=-1
.d) r=-1
This is not in the assignment This is a sample final exam question that will help you understand the assignment

Answer the questions below , you do not have to use the precise definitions
a) Give an example of a percentile of a variable
b) How can you always estimate a percentile of an observed value by using a list of many random observations of that variable, give an example
c) If an observed value has a z score of 10 what do know about the percentile of the observed value
d) What is another way of finding a percentile of an observed test stat if you are assuming the null hypothesis is true and you only have one test stat, Give an example
e) What is the relationship between p-value and the amount of evidence against H0 and for H1
f) What is another way of a finding a percentile of a p-value if you are assuming the null hypothesis is true and you only have one test stat , give an example
Answer (Note you can change the numbers)

a) If the 97.5th of percentile of a variable is 1.96 then 97.5% of values are below 1.96
b) Work out the proportion of observations on the list that are less than the observed value , for example if you observe the value of 1.96 and 97.5% of the values on the list are less than 1.96 then 1.96 must be the 97.5th percentile
c) It must be close to 1
d) Use the distribution of the test stat , For example if the test stat has a z distribution and the test stat is 1.96 then P(Z<1.96) = 0.975 using the z table
e) The lower the p-value the more evidence that you have against the null hypothesis and for the alternative hypothesis
f) If the null Hypothesis is true, the percentile of p-value is just the p-value, For example if the p-value is 0.05 then it is then 5% of other p-values will above below 0.05,

Thi is not part of the assignment it is an explanation about why the course is so strange page 1 of 2

the 95% confidence interval formula for the sample mean when n=100
is
that the population mean µ is between
sample mean – 1.984 standard errors and sample mean +1.984 standard errors
Finding a confidence interval is a deductive method because you already know all the steps of the process before you get the data

You can verify that 95% of sample means lie within 1.984 standard errors of the population mean by letting x= 1.984 and x =1.984 in the formula below, you will get the percentiles 0.025 and 0.975
(note x^2 is the same as x2 also note the formula is very long but the chart is simple, the value has already been worked out and put into a t-table t99,0.025 =1.984)

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Thi is not part of the assignment it is an explanation about why the course is so strange page 2 of 2

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