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Hi,I have a final tomorrow for economics and statistics class. The questions lasts for 180 minutes and I need answers in that timeframe. It will start at 9:30 P.M. (Washinntgon D.C.). Thursdy. Oct. 21, 2021.I am attaching the final review of the material and guidlience along with practice questions with its answers which will be similar to the final. Please make sure you read them and understand them so you can answer the questions in the final.Please let me know if you have any questions.

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Contact me on whats app at +966599331424

or by email at mohd.ota@gmail.com

What is the format of the final exam?

What materials should I cover?

How do I answer the question?

Topic 11: Final Exam Preparation

Deakin University

1/6

What is the format of the final exam?

What materials should I cover?

1

What is the format of the final exam?

2

What materials should I cover?

3

How do I answer the question?

How do I answer the question?

2/6

What is the format of the final exam?

What materials should I cover?

How do I answer the question?

Final exam format

The final exam is an open book timed online exam.

Please check your exam timetable carefully.

The approximate time to complete the exam is 2 hours and 15

minutes as with standard exams. You have 45 extra minutes to

upload your answers. So, a total of 3 hours will be provided.

You should carefully read all the instructions on the exam paper.

3/6

What is the format of the final exam?

What materials should I cover?

How do I answer the question?

Final exam format

The exam consists of two sections.

Section A is about economics (microeconomics and macroeconomics

combined) and is worth 60% of the total marks. All questions in

Section A carry equal marks.

Section B is about statistics and is worth 40% of the total marks. All

questions in Section B carry equal marks.

You will choose any two of the three questions in section A and

any one of the two questions in section B.

We will provide relevant statistics (but not economics) formulas and

cumulative standardised normal distribution table.

To satisfy the hurdle requirement, you must achieve at least 50% of

the marks in the final exam.

4/6

What is the format of the final exam?

What materials should I cover?

How do I answer the question?

What materials should I cover?

The final exam covers all of the topics weve studied in this trimester.

To help you study for the exam, we provide you with 16 extra practice

questions in the form of Problem Set 11 (with suggested solutions).

Please revise these questions along with the previous problem sets and

lecture slides.

5/6

What is the format of the final exam?

What materials should I cover?

How do I answer the question?

How do I answer the question?

Read a question carefully and make sure you understand it before

answering.

If you need to make assumptions, state them clearly in your responses.

Base your arguments on economic reasoning.

Use diagrams to support your argument whenever appropriate.

Write down the intermediate steps to reach the final answer, as

partial marks may be awarded for these.

Good responses are usually clear, concise, and to the point.

6/6

Problem set 11 solutions

Problem 1. Suppose the price elasticity of demand for electricity is 0.2 in the short run

and 0.7 in the long run. What happens to the quantity demanded for electricity in the

short run as the price of electricity increases from $0.25 to $0.40 per kilowatt hour? In the

long run?

Solution. The percentage change in price is (0.40-0.25)/(0.25), which equals 0.6. In the

short-run the price elasticity of demand for electricity is 0.2. Hence the percentage change

in quantity demanded of electricity is (0.2×0.6) = 0.12. In the long run, the percentage

change in quantity demanded of electricity is (0.7×0.6) = 0.42. This implies that the demand for the electricity substitute will rise in both the short run and long run, but more

so in the long run.

Problem 2. Suppose the income elasticity of demand for smartphones is 2 and the income

elasticity of demand for house painting is 0.8. Compare the impact of smartphones and

house painting of a recession that reduces consumer income by 5 percent.

Solution. Because smart phones have an income elasticity of demand of 2, we know that

they are a normal good, because the coefficient is positive. The same is true for house

painting, with a coefficient of 0.8. However, the income elasticity of house painting is

clearly lower than that of smart phones. This means that a reduction of income from a

recession will have a greater impact on smart phones than it will on house painting.

Problem 3. After economics class one day, your friend suggests that taxing food would

be a good way to raise revenue because the demand for food is quite inelastic. In what

sense is taxing food a good way to raise revenue? In what sense is it not a good way

to raise revenue?

Solution. Since the demand for food is inelastic, a tax on food is a good way to raise

revenue because it doesnt result in much of a deadweight loss. Thus, taxing food is less

inefficient than taxing other things. But it isnt a good way to raise revenue from an equity

point of view, since poorer people spend a higher proportion of their income on food, so

the tax would hit them harder than it would hit wealthier people.

1

Problem 4. Some economists argue that private firms will not undertake the efficient

amount of basic scientific research. Explain why this is so.

Solution. Since knowledge is a public good, the benefits of basic scientific research are

available to many people. The private firm doesnt take this into account when choosing

how much research to undertake; it only considers what it will earn, so it produces less

basic research than the efficient amount.

Problem 5. Suppose that a market is described by the following supply and demand

equations: P = Q and P = 100 ? Q.

1. Solve for the equilibrium price and quantity.

2. Suppose that a tax of $10 is placed on sellers, so the new supply equation is P =

10 + Q. What happens to the price received by sellers, the price paid by buyers, the

quantity sold, and the tax revenue collected by the government?

3. Calculate the deadweight loss from the tax.

Solution.

1. Set the two equations equal to each other to find the equilibrium quantity. Thus

Q = 100 ? Q or, 2Q = 100, hence Q = 50. Substitute this value of Q into the

demand equation and solve for the equilibrium price. This is P = 50.

2. Set the new supply equation equal to the demand to find the new equilibrium quantity, so 10 + Q = 100 ? Q, or 2Q = 90, or Q = 45. The price the buyers pay is

100 ? 45 = $55. The price the sellers receive is 55 ? 10 = $45. The tax revenue is

10 × 45 = $450.

2

3. The deadweight loss from the tax is 1/2 × (50 ? 45) × 10 = $25.

Problem 6. A competitive firm receives $500 in total revenue and has marginal revenue

of $10. What is the average revenue, and how many units were sold?

Solution. A firm in a competitive market has the P = AR = MR. Given that the MR is

$10, then 50 units must have been sold, and the average revenue is also $10.

Problem 7. A profit-maximizing firm in a competitive market is currently producing 100

units of output. It has average revenue of $10, average total cost of $8, and fixed costs of

$200.

1. What is its profit?

2. What is its marginal cost?

3. What is its average variable cost?

4. Is the efficient scale of the firm more than, less than, or exactly 100 units?

Solution.

1. The profit is equal to ( ARATC ) × Q. This is (108) × 100, or $200.

2. The marginal cost has to equal the marginal revenue at the profit-maximising level

of output, hence it is $10.

3. Recall that ATC = AFC + AVC. If ATC is $8, and AFC is FC/Q, or $2, then AVC

must be $6.

4. The efficient level of output is less than 100. The efficient level occurs when the ATC

is minimised. This is where MC = ATC. Given MC ($10) is greater than ATC ($8)

the firm must be producing at an output level higher than the efficient level.

Problem 8. A company obtains the following information about the demand and production costs of its new product:

Demand: P = 100 ? Q

Marginal Revenue: MR = 100 ? 2Q

Marginal Cost: MC = 10 + Q

1. Find the price and quantity that maximizes the companys profit.

3

2. Find the price and quantity that would maximize social welfare.

3. Calculate the deadweight loss from monopoly.

Solution.

1. Set MR = MC to find the monopoly quantity. Thus, 100 ? 2Qm = 10 + Qm , or

Qm = 30. Substitute this value into the demand equation to find the monopoly

price, Pm = 100 ? 30 = 70.

2. Set P = MC to find the competitive quantity, so 100 ? Qc = 10 + Qc , or Qc = 45.

The competitive price is equal to the marginal cost at the competitive quantity, so

Pc = 10 + 45 = 55. The competitive price and quantity maximize social welfare.

3. The marginal cost at the monopoly quantity is 10 + 30 = 40. The deadweight loss

from monopoly is 1/2 × (45 ? 30) × (70 ? 40) = 225.

Problem 9. Consider the relationship between monopoly pricing and price elasticity of

demand:

1. Explain why a monopolist will never produce a quantity at which the demand curve

is inelastic. (Hint: If demand is inelastic and the firm raises its price, what happens

to total revenue and total costs?)

2. Draw a diagram for a monopolist, precisely labeling the portion of the demand

curve that is inelastic. (Hint: The answer is related to the marginal-revenue curve.)

Solution.

4

1. A monopolist always produces a quantity at which the demand curve is elastic. If

the firm produced a quantity for which the demand curve were inelastic, then if the

firm raised its price, quantity would fall by a smaller percentage than the rise in

price, so revenue would increase. Since costs would decrease at a lower quantity,

the firm would have higher revenue and lower costs, so profit would be higher.

Thus, the firm should keep raising its price until profits are maximised, which must

happen on an elastic portion of the demand curve.

2. On the inelastic portion of the demand curve, marginal revenue is negative. Increasing quantity requires a greater percentage reduction in price, so revenue declines. Since a firm maximises profit where marginal cost equals marginal revenue,

and marginal cost is never negative, the profit-maximising quantity can never occur

where marginal revenue is negative, so can never be on an inelastic portion of the

demand curve.

Problem 10. Why do you think households purchases of new housing are included in the

investment component of GDP rather than the consumption component? Can you think

of a reason why households purchases of new cars should also be included in investment

rather than in consumption? To what other consumption goods might this logic apply?

Solution. Purchases of new housing are included in the investment portion of GDP because housing lasts for a long time. For the same reason, purchases of new cars could be

thought of as investment, but by convention, they are not. The logic could apply to any

durable good, such as household appliances. However, the lifetime of housing is much

greater than other household goods and for this reason it is counted as investment.

Problem 11. Using a diagram of the labor market, show the effect of an increase in the

minimum wage on the wage paid to workers, the number of workers supplied, the num5

ber of workers demanded, and the amount of unemployment. Is this type of unemployment frictional unemployment or structural unemployment? Explain.

Solution. The figure shows a diagram of the labor market with a binding minimum wage.

The initial equilibrium with minimum wage m1 has quantity of labor supply L1S greater

than the quantity of labor demanded L1D , with unemployment equal to L1S ? L1D . An

increase in the minimum wage to m2 leads to an increase in the quantity of labor supplied

to L2S and a decrease in the quantity of labor demanded to L2D . As a result, unemployment

increases as the minimum wage rises.

Unemployment of this sort is sometimes called structural unemployment, because the

number of jobs available in the labor market is insufficient to provide a job for everyone

who wants one. By contrast, the unemployment that results from the process of matching

workers and jobs is called frictional unemployment.

Problem 12. Suppose that changes in bank regulations expand the availability of credit

cards so that people need to hold less cash.

1. How does this event affect the demand for money?

2. If the RBA does not respond to this event, what will happen to the interest rate?

3. If the RBA wants to keep the interest rate stable, what should it do?

Solution.

1. If people need to hold less cash, the demand for money shifts to the left, since there

will be less money demanded at any price level.

6

2. If the RBA does not respond to this event, the shift to the left of the demand for

money combined with no change in the supply of money leads to a decline in the

interest rate, which means the price level rises, as shown in the figure below.

3. If the Fed wants to keep the interest rate stable, it should reduce the money supply

from MS1 to MS2 . This would cause the supply of money to shift to the left by

the same amount that the demand for money shifted, resulting in no change in the

value of money and the interest rate.

Problem 13. For each of the following events, explain the short-run and long-run effects

on output and the price level, assuming policymakers take no action.

1. The stock market declines sharply, reducing consumers wealth.

2. Yarra Valley grape farms suffer a prolonged period of dry weather.

3. Firms become very optimistic about future business conditions and invest heavily

in new capital equipment.

Solution.

1. When the stock market declines sharply, wealth declines, so the aggregate-demand

curve shifts to the left. In the short run, the economy moves from point A to point

B, as output declines and the price level declines. In the long run, the short-run

aggregate-supply curve shifts to the right to restore equilibrium at point C, with

unchanged output and a lower price level compared to point A.

7

2. If Yarra Valley grape farms suffer a prolonged period of dry weather, the grape

harvest will be reduced. This is represented in the figure below by a shift to the left

in the short-run aggregate-supply curve. The equilibrium changes from point A to

point B, so the price level rises and output declines.

3. The investment boom will increase the long-run aggregate supply because higher

investment today means a larger capital stock in the future, thus higher productivity

and output. Thus, the long-run and short-run aggregate-supply curves shift to the

right. The economy moves from point A to point B, as output rises and the price

level declines. Yes! This is a very difficult problem.

8

Problem 14. The projected number of persons in different living arrangements in Australia as at 30 June 2016 are as follows.

Category (x)

Number of persons (000)

Couple with children (1)

Couple without children (2)

One parent male (3)

One parent female (4)

Other (5)

Total

2473

2706

185

914

109

6387

Source: Australian Bureau of Statistics, Household and Family Projections, Australia, 20162026, 2012, cat.

no. 3236.0, ABS, Canberra

1. Construct the probability distribution of X and present it in graphical form.

2. What is the projected most likely category of living arrangement in Australia in

2016?

3. What is the probability that a randomly selected person is from a one parent female

living arrangement category?

4. What is the probability that a person is randomly selected from families living as a

couple?

5. What is the expected number and variance of persons in different living arrangements in Australia?

Solution.

9

1. Let X be the number of persons in different living arrangements in Australia.

X

P( X = x )

1

0.3872

2

0.4237

3

0.0290

4

0.1431

5

0.0171

The probability distribution of X is shown below:

2. The most likely category of living arrangement in Australia is couple without children (2).

3. The probability that a randomly selected person is from a one parent female is

0.1431.

4. P (couple) = P (Couple with children) + P (Couple without children) = 0.3872 +

0.4237 = 0.8109.

5. The following table provides the calculation of mean and variance:

x

p (x)

xp ( x )

x?µ

( x ? µ )2

( x ? µ )2 p ( x )

1

2

3

4

5

0.3872

0.4237

0.0290

0.1431

0.0171

0.387

0.847

0.087

0.572

0.086

-0.980

0.021

1.021

2.021

3.021

0.959

0.000

1.041

4.082

9.123

0.371

0.000

0.030

0.584

0.156

?2 = 1.142

µ = 1.98

Thus, the expected number of persons in different living arrangements in Australia

is 1.98 and the variance is 1.142.

10

Problem 15. The final marks in a statistics course are normally distributed with a mean of

70 and a standard deviation of 10. The professor must convert all marks to letter grades.

The professor wants 10% of the students to receive an A, 30% a B, 40% a C, 15% a D and

5% an F. Determine the cut-offs for each letter grade.

Solution. Let X be the final exam mark. X ~ Normal(70, 10). Let x A , x B , xC and x D be the

?70

cutoffs for grades A, B, C and D, respectively. Therefore zi = xi 10

, i = A, B, C, D.

?70

= 1.28, or x A = 82.8.

P (Z < z A ) = 0.90 implies z A = 1.28. Thus, xA10
?70
P (Z < zB ) = 0.60 implies zB = 0.25. Thus, xB10
= 0.25, or xB = 72.5.
?70
= ?0.84, or xC = 61.6.
P (Z < zC ) = 0.20 implies zC = ?0.84. Thus, xC10
?70
P (Z < zD ) = 0.05 implies zD = ?1.645. Thus, xD10
= ?1.645, or xD = 53.55.
Problem 16. An economist wanted to investigate the relationship between office rents
and vacancy rates. Accordingly, he took a random sample of monthly office rents ($000)
and the percentage of vacant office space in 30 different cities. The computer printout is
given below.
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
0.5396
A
0.2658
2.8732
30
ANOVA
Regression
Residual
Total
Intercept
Vacancy rate
df
1
28
29
Coefficients
B
-0.304
SS
94.94
231.15
326.09
MS
94.94
8.26
Standard Error t Stat
1.143 18.061
C -3.391
F Significance F
11.50
0.0021
P-value
0.000
0.002
1. Using the information from the printout, calculate the value of A, B, and C.
2. Find the sample regression line and interpret the coefficients.
11
3. Can we conclude at the 5% significance level that higher vacancy rates result in
lower rents?
4. The economist concluded that higher vacancy rates had caused the office rents to
fall. Do you think his conclusion is correct? If not, why?
Solution.
1. From the ANOVA table, the sum of squared total is SST = 326.09, and the sum of
squared for regression is SSR = 94.94. Thus, the value of A is R2 = SSR/SST =
94.94/326.09 = 0.2911.
From the coefficients table, the standard error of b0 is sb0 = 1.143, and the t statistic
is tb0 = 18.061. It follows that the intercept coefficient B is b0 = t0 × sb0 = 18.061 ×
1.143 = 20.64.
Similarly, the coefficient for vacancy rate is b1 = ?0.304, and the associated t statistic
is tb1 = ?3.391. Thus, the standard error of vacancy rate C is sb1 = b1 /tb1 =
?0.304/ ? 3.391 = 0.09.
2. The estimated regression equation is y? = 20.64 ? 0.304x. The slope indicates that
for each additional one percentage point increase in the vacancy rate, rents on average decrease by 0.304 thousand dollars. The y-intercept is 20.64, which has no real
meaning.
3. The appropriate test is a left one tail test, H0 : ? 1 = 0, H1 : ? 1 < 0. The test statistic is
t = ?3.391 and the p-value for a one-tail test is 0.002/2 = 0.001. Therefore, the null
hypothesis should be rejected at the 5% significance level and one could conclude
that higher vacancy rates result in lower rents (in a statistical sense).
4. While it seems reasonable to conclude that higher vacancy rates cause lower rents,
this conclusion may not be entirely true. It is possible that the rents and vacancy
rates are both affected by the state of the economy and the rents fall and vacancy
rates rise when the economic condition worsens. It is also theoretically possible that
lower rents cause higher vacancy rates because owners hold back on leasing space
when the rents are unfavourable. Further analysis would be needed to establish the
veracity of this conclusion.
12
Unit Code: MPE781 Unit Name: Economics for Managers Final Examination T2, 2021
__________________________________________________
DEAKIN UNIVERSITY
FACULTY OF BUSINESS AND LAW
Department of Economics
FINAL EXAMINATION TRIMESTER 2, 2021
Unit Code: MPE781
Unit Name: Economics for Managers
Estimated Reading Time: 15 minutes
Estimated Working Time: 2 hours
Estimated time for preparing and submitting your final responses to CloudDeakin Dropbox:
45 minutes
This is an Open Book Scheduled Online Release Examination. You must upload your final
responses as a Microsoft Word Doc and a pdf file to CloudDeakin Dropbox within 3 hours
from the start time scheduled in the exam timetable.
This exam consists of 5 questions including 3 questions in Section A and 2 questions in
Section B. Answer any 2 questions in Section A and any 1 question in Section B. This exam
paper carries a total of 60 marks. (This is converted to 60% of your total assessment in this
unit).
Preparing and submitting your answers:
Download the exam answer sheet word document and save it on your computer using the
file name: your-student-ID_ unit-code; A hypothetical example: 123456789_ MPE781.
Input your answers in that document by typing your response below each question number.
Keep saving your work regularly as you make progress towards completing your exam.
Please also insert appropriate diagrams and calculations if necessary in the answer
document. Legibly draw/hand-write relevant graphs or calculations on a piece of white
paper, scan it and insert it in the document along with your typed response to each question.
You are allowed to use a calculator to aid your work.
For instructions on scanning and inserting images in the word document, please refer to
Exam Preliminary Information Document that was released on the unit site prior to the exam
period.
Upload the completed exam answer sheet word document along with a pdf copy of the same
in the CloudDeakin Dropbox prior to cut-off time. Check that you uploaded the correct file.
Late submissions will not be marked.
If you encounter any technical issues with CloudDeakin, please contact the IT Service Desk
online or via phone (1800 463 888; +61 5227 8888 if calling from outside Australia) and
record your ticket number as evidence of technical issues during the examination period.
In the unlikely event that you cannot upload your completed exam paper, email it as an
attachment to your unit chair xuan.nguyen@deakin.edu.au within the submission time.
NOTE: It is important that you work individually on this exam. Your submission will be
reviewed for the purposes of detecting collusion and/or plagiarism.
Page 1 of 6
Unit Code: MPE781 Unit Name: Economics for Managers Final Examination T2, 2021
__________________________________________________
SECTION A
This section consists of 3 questions carrying equal marks. Please answer any 2 of the 3
questions. You should provide relevant diagrams while answering the questions.
Question 1
John runs the only juice stall in the shopping centre. The following equations show
Johns demand, marginal revenue, total cost, and marginal cost, respectively:
Demand: P = 20 Q
Marginal revenue: MR = 20 2Q
Total cost: 5 + 4Q
Marginal cost: MC = 4
where Q is the quantity (bottles) of juice and P is the price.
a) How many bottles of juice does John sell? At what price are they sold? How much
profit does John make?
b) What is the price elasticity of demand at Johns monopoly quantity and price?
c) Calculate the consumer surplus, producer surplus, total surplus, and deadweight
loss.
[6+6+6 = 18 marks]
Question 2
Suppose that the government imposes a tax on cigarettes to reduce smoking.
a) Should this tax be imposed on sellers or buyers? Explain using both words and a
diagram.
b) Will this tax be more effective or less effective in reducing cigarettes consumption
if the demand for cigarettes is relatively inelastic? (Hint: Draw two figures, side by
side, with the same supply curve and different demand curves.)
c) Who is going to bear greater tax burden, buyers or sellers, if the demand for
cigarettes is relatively inelastic? Explain with the help of a figure.
[6+6+6 = 18 marks]
Question 3
Using the AS/AD model, discuss the likely short-run and long-run impacts of the
following events with proper diagram(s), assuming that the government takes no
further action:
a) An income tax rebate, giving each worker $2,000 (starting from the fullemployment level).
b) A contractionary monetary policy in which the interest rate is raised (starting from
the full-employment level).
[9+9 = 18 marks]
Page 2 of 6
Unit Code: MPE781 Unit Name: Economics for Managers Final Examination T2, 2021
__________________________________________________
SECTION B
This section consists of 2 questions carrying equal marks. Please answer any 1 of the 2
questions. Useful statistics formulae and a cumulative standardised normal distribution
table can be found in the subsequent pages of this exam paper.
Question 4
The manager of a firm that owns several stores in Australia wants to examine the effects
of the spending on corporate social responsibility (CSR) on profitability across stores.
He collects data on CSR and profit ($000s) from 20 stores located in different cities,
and estimates the following regression equation:
!"#$%&! = (" + (# *+,! + -!
The output when using Excel to estimate the equation is given below:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.47
R Square
A
Adjusted R Square
0.18
Standard Error
44.37
Observations
20
ANOVA
Regression
Residual
Total
Intercept
CSR
df
SS
MS
F
Significance F
1
18
19
10203.64
35440.11
45643.75
10203.64
1968.89
5.18
0.04
Coefficients
B
2.63
Standard Error
31.38
C
t Stat
6.41
2.28
P-value
0.00
0.04
a) Find the value of A, B and C, and interpret their meanings.
b) Find the simple regression line and interpret the coefficients.
c) Can the manager conclude that there is a positive relationship between spending on
CSR and profit at (i) 1% significance level, (ii) 5% significance level, and (iii) 10%
significance level? Briefly explain your answer.
d) Based on this result, the manager concludes that stores should increase spending on
CSR to improve profitability. Why might the manager be wrong?
[6+6+6+6 = 24 marks]
Page 3 of 6
Unit Code: MPE781 Unit Name: Economics for Managers Final Examination T2, 2021
__________________________________________________
Question 5
The amounts of money ($) spent by 14 students for their breakfast this morning are:
10, 9, 7, 5, 10, 9, 10, 3, 5, 7, 8, 7, 7, 10
a. Calculate the sample mean, median, and mode. Interpret these values. What type
of distribution does it represent, symmetric, skewed to the right or skewed to
the left?
b. Calculate the sample first quartile, third quartile, and interquartile range.
Interpret these values.
c. Calculate the sample standard deviation. Interpret this value.
[8+8+8 = 24 marks]
Page 4 of 6
Unit Code: MPE781 Unit Name: Economics for Managers Final Examination T2, 2021
__________________________________________________
USEFUL STATISTICS FORMULAE
Sample Mean: ./ =
?"
!#$ %!
&
'
((%
?" (% )%+ )%
!
Sample Variance: + = &)# = !#$&)#
++. = ?&!-#(.! ? ./)' = ?&!-# .!' ? 4./ '
Sample Standard Deviation: + = ?+ '
Sample Covariance: 6#7(., 9) =
((%.
&)#
=
=
%
+%
?"
!#$ %! )&%
&)#
+
+
?"
!#$(%! )% )(.! ). )
&)#
=
++
?"
!#$ %! .! )&% .
&)#
++.9 = ?&!-#(.! ? ./)(9! ? 9/ ) = ?&!-# .! 9! ? 4./9/
Sample Coefficient of Correlation: " =
/01(%,.)
(& ('
=
((%.
?((%?((.
General Addition Rule of Probability: !(: #"
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