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TSTA602 Workshop 3 Problem Set
1. Consider an investment of $100,000 that declined to a value of $50,000 at the end of the first year
and recovered back to $100,000 at the end of the second year. Calculate the arithmetic mean and the
geometric mean of the annual rates of return of this investment, and comment on your results.
2. Two populations, A and B, have the same coefficient of variation. If A’s mean is four times as large
as B’s, then A’s standard deviation is:
a. twice as large as B’s
c. four times as large as B’s
b. half as large as B’s
d. unknown from the given information
3. There are 7 members of the crew of a space shuttle. On earth they weigh 98, 77, 63, 101, 85, 49 and
94 kilograms. Find the mean, median, population standard deviation and range of the weights on
Earth.
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4. The following information shows the calories and fat in 500ml (approx.) drinks available from a
number of outlets:
a. For each variable, compute the mean, median, mode, first quartile and third quartile.
b. For each variable, compute the sample variance, sample standard deviation, range, interquartile
range, coefficient of variation. Are the data skewed? If so, how?
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5. A bank branch located in a commercial district of a city has developed an improved process for serving
customers during the noon-1pm lunch period. The waiting time, in minutes of a sample of 15 customers
during this hour is recorded over a week. The results are:
a. Calculate the mean, median, first quartile and third quartile
b. Calculate the variance, sample standard deviation, range, interquartile range, coefficient of
variation.
c. Are the data skewed? If so, how?
d. A customer walks into the branch during the lunch hour and asks the branch manager how long a
wait she can expect. The branch manager replies, “Almost certainly less than five minutes.” On the
basis of your results to parts a. –c., comment on the manager’s rely.
6. A population of TSTA602 students is known to have a mean final mark of 65 and a standard
deviation of 5. The population is known to be bell-shaped. Describe the distribution of final marks.
Is it likely that a student will fail this unit? Is it likely that a student will achieve above 80?
7.
a. Calculate the 5-number summary for the following data:
5 4 7 13 20 9 12 21 23 19 17
b. Discuss the skewness of the data.
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8. An owner of a restaurant is interested in examining the demand for dessert over a given time
period. She is worried that the size of entrées is too large, therefore affecting whether or not patrons
order dessert. If this is the case, it would have an impact on her profit. She collects data on whether
a dessert is ordered and whether an entrée is ordered for a sample of 1000 patrons. She finds the
following:
a. Among the patrons who do not order dessert, what is the percentage of those having ordered
entrée? Can the owner make a decision on the size of the entrée based on this percentage? Explain.
b. Produce a side-by-side bar chart and a stacked bar chart based on this contingent table using MS
Excel. Comment on these two charts. Discuss again whether the owner should reduce the size of the
entrée.
9. Use the calories and fat data in question 4 (see data in WS3.xlsx), compute
a. The sample covariance
b. The coefficient of correlation
Which do you think is more informative in expressing the relationship between calories and fat?
Explain. What conclusion do you reach about the relationship between calories and fat? Produce a
scatter plot using MS Excel and comment on the result.
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TSTA602 Workshop 8 Problem Set
1. The following data represent the number of days absent per year in a population of six employees
of a small company: 1 3 6 7 9 10. Assuming that you randomly select a sample of n=2 with replacement
and construct the sampling distribution of the mean. Compute the mean of all the sample means and
also compute the population mean. Are the equal? What is this property called?
2. The amount of time required for an oil and filter change on an automobile is normally distributed
with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is
selected.
a. What is the probability that a sample mean is between 45 and 52 minutes?
b. What is the probability that the sample mean is between 39 and 48 minutes?
3. An automatic machine filling soup cans has μ = 500ml and σ = 20ml. A sample of 64 cans is
inspected.
a. What is the probability that a sample mean fill is greater than 504.5ml?
b. What is the probability that a sample mean fill is less than 499.5ml?
4. A sample of 364 employees’ hourly wages was observed. The mean wage of all employees in the
firm is $17.50 per hour with a standard deviation of $5.20. The observed sample mean will lie within
which two values, symmetric about the mean with a 92% probability?
5. The quality control manager at a light bulb factory needs to estimate the mean life of a large
shipment of light bulbs. The standard deviation is 100 hours. A random sample of 64 light bulbs
indicated a sample mean life of 350 hours.
a. Construct a 95% confidence interval estimate of the population mean life of light bulbs in
this shipment and interpret your result.
b. Do you think that the manufacturer has the right to state that the light bulbs last an average
of 400 hours? Explain.
c. Must you assume that the population of light bulb life is normally distributed? Explain.
Registered Higher Education Provider
TEQSA PRV12059 | CRICOS Code: 02491D
Top Education Group Ltd ACN 098 139 176 trading as Australian
National Institute of Management and Commerce (IMC)
TSTA602
Quantitative Methods
for Accounting and
Finance
Modern Business
Statistics, 7e
Anderson, Sweeney, Williams,
Camm, Cochran, Fry, Ohlmann
© 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Contact Details
• Lecturer: Dr Biplob Chowdhury
• Email: biplob.chowdhury@imc.edu.au
• Consultation: by email and appointment only
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Chapter 1: Data and Statistics
Statistics
Applications in Business and Economics
Data Sources
Descriptive Statistics
Statistical Inference
Statistical Analysis Using Microsoft Excel
Analytics
Big Data and Data Mining
Ethical Guidelines for Statistical Practice
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Chapter 2, Part A
Descriptive Statistics: Tabular and Graphical Displays
Summarizing Data for a Categorical Variable
Categorical data use labels or names to identify categories of like items.
Summarizing Data for a Quantitative Variable
Quantitative data are numerical values that indicate how much or how many.
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Chapter 2, Part B
Descriptive Statistics: Tabular and Graphical Displays
Summarizing Data for Two Variables Using Tables
Summarizing Data for Two Variables Using Graphical Displays
Data Visualization: Best Practices in Creating Effective Graphical Displays
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Chapter 3, Part A
Descriptive Statistics: Numerical Measures
Measures of Location
Measures of Variability
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Chapter 3, Part B
Descriptive Statistics: Numerical Measures
Measures of Distribution Shape, Relative Location, and Detecting Outliers.
Five-Number Summaries and Boxplots
Measures of Association Between Two Variables
Data Dashboards: Adding Numerical Measures to Improve Effectiveness
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Chapter 4
Introduction to Probability
Experiments, Counting Rules, and Assigning Probabilities
Events and Their Probabilities
Some Basic Relationships of Probability
Conditional Probability
Bayes’ Theorem
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Chapter 5
Discrete Probability Distributions
Random Variables
Developing Discrete Probability Distributions
Expected Value and Variance
Bivariate distributions and Covariance
Financial Portfolios
Binomial Probability Distribution
Poisson Probability Distribution
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Chapter 6
Continuous Probability Distributions
• Uniform Probability Distribution
• Normal Probability Distribution
• Exponential Probability Distribution
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Chapter 7
Sampling and Sampling Distributions
Selecting a Sample
Point Estimation
Introduction to Sampling Distributions
Sampling Distribution of
x
• Sampling Distribution of p
• Other Sampling Methods
• Big data and Errors in Sampling
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Chapter 8
Interval Estimation
Population Mean: σ Known
Population Mean: σ Unknown
Determining the Sample Size
Population Proportion
Big data and Interval estimation
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Chapter 9
Hypothesis Testing
Developing Null and Alternative Hypotheses
Type I and Type II Errors
Population Mean: σ Known
Population Mean: σ Unknown
Population Proportion
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Chapter 14, Part A
Simple Linear Regression
Simple Linear Regression Model
Least Squares Method
Coefficient of Determination
Model Assumptions
Testing for Significance
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Chapter 14, Part B
Simple Linear Regression
Using the Estimated Regression Equation for Estimation and Prediction
Excel’s Regression Tool
Residual Analysis: Validating Model Assumptions
Outliers and Influential Observations
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Chapter 15
Multiple Regression
Multiple Regression Model
Least Squares Method
Multiple Coefficient of Determination
Model Assumptions
Testing for Significance
Using the Estimated Regression Equation for Estimation and Prediction
Categorical Independent Variables
Residual Analysis
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How will I be Assessed
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Requirements to Pass the Unit
Requirements to Pass the Unit
To achieve a passing grade in this unit a student must:
(a)Attempt all within-term assessment tasks to the satisfaction of the lecturerin-charge;
(b)Attend the final examination and submit a completed examination script;
and
(c)Achieve an overall mark of at least 50% in the unit.
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Final Exam
Instructions:
Answer all THREE (3) Questions. Please type your answers immediately following each
question. Be sure to read all instructions and questions carefully before answering. Make use
of formulae and graphs to clarify your answers, as and when possible. Show all steps when
calculations are involved.
Section
Question format
Number of questions
Worth
Each Question
comprises of multiple
parts.
Answer all THREE (3)
questions.
100 marks
Total
100 marks
Time Management:
Time Allowed: 3 hours – 180 minutes
Total marks: 100 marks
The examination counts for 40 percent of the marks for this unit.
But!!Read Chapter Carefully
Week
1
2
3
4
5
6
7
8
9
10
11
Topic/s and activities
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 14
Chapter 15
What To Study For The Final Exam?
• Workshop questions
• Lecture material
• Assignment
• Please do not study previous exam papers
3-hour
Final
Exam
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