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Assessment Task – Tutorial Questions
Unit Code: HI6007
Unit Name: Statistics for Business Decisions
Assignment: Tutorial Questions Assignment
Due: week 13
Weighting: 50%
Purpose: This assignment is designed to assess your level of knowledge of the key topics covered in
this unit
Unit Learning Outcomes Assessed.:
1. Understand appropriate business research methodologies and how to apply them
to support decision-making process.
2. Understand various qualitative and quantitative research methodologies and
techniques.
3. Explain how statistical techniques can solve business problems;
4. Identify and evaluate valid statistical techniques in a given scenario to solve
usiness problems;
5. Explain and justify the results of a statistical analysis in the context of critical
easoning for a business problem solving
6. Apply statistical knowledge to summarize data graphically and statistically, either
manually or via a computer package;
7. Justify and interpret statistical/analytical scenarios that best fits business solution;
8. Explain and justify value and limitations of the statistical techniques to business
decision making and;
9. Explain how statistical techniques can be used in research and trade publication
Description: Each week students were provided with three tutorial questions of varying degrees of
difficulty. The tutorial questions are available in the Tutorial Folder, for each week, on Blackboard.
The interactive tutorials are designed to assist students with the process, skills and knowledge to
answer the provided tutorial questions. Your task is to answer a selection of tutorial question for
weeks 1 to 11 inclusive and submit these answers in a single document.
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The questions to be answered are;
Question 1: Week 2 Question 4 (7 Marks)
a. The following data shows the results for 20 students in one of the post graduate unit.
XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXX XXXXXXXXXX
Based on the information given you are required to
i. Compute the mean, median and mode XXXXXXXXXXmarks)
ii. Compute the first and third quartiles XXXXXXXXXXmark)
iii. Compute and interpret the 90th percentile XXXXXXXXXXmark)
. In your own word, explain what is inferential statistics with relevant examples.
XXXXXXXXXXmarks)
Question 2: Week 3 Question 4, (7 Marks)
a. Holmes Institute conducted a survey about International Students in Melbourne. The
survey results are given in the table below.
Applied to more than 1 university
Yes No
Age Group
23 and under XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
36 and over 51 169
i. Prepare a joint probability table XXXXXXXXXXmark)
ii. Given that a student applied to more than 1 university, what is the probability that
the student is 24-26 years old XXXXXXXXXXmark)
iii. Is the number of universities applied to independent of student age? Explain
(2 marks)
. Assume, North Origano, is a country with highest domestic violence cases (approximately
5 cases per 1000 families). Working with counselors, a researcher developed the
following probability distribution for x= the number of new clients for counseling for 2021.
x f(x)
10 0.05
20 0.10
30 0.10
40 0.20
50 0.35
60 0.20
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i. Compute the expected value and variance of x. XXXXXXXXXX3 marks)
Question 3: Week 8 Question 3, (11 Marks)
According to the Annual survey of drugs expenditure in country X, the annual expenditure for
prescription drugs is $838 per person in the Northeast region of the country. A sample of 60 individuals
in the Midwest shows a per person expenditure for prescription drugs of $745. Further, it is given that
the population standard deviation of $300.
I. Formulate hypotheses for a test to determine whether the sample data support the
conclusion that the population annual expenditure for prescription drugs per person is lower
in the Midwest than in the Northeast and Identify whether it is a two-tail test or a one tail test
(Left or right tail XXXXXXXXXXmarks)
II. Decide the suitable test statistics and justify your selection XXXXXXXXXXmark)
III. Calculate the value of the relevant test statistics and identify the P value XXXXXXXXXXmarks)
IV. Based on the p value in part (III), at 99% confidence level, decide the decision criteria. (1 mark)
V. Make the final conclusion based on the analysis XXXXXXXXXXmarks)
Question 4: Week 9 Question 2, (11 Marks)
The gasoline price often varies a great deal across different regions across country X. The following
data show the price per gallon for regular gasoline for a random sample of gasoline service station for
three major
ands of gasoline (A, B and C) located in 10 metropolitan areas across the country X.
A B C
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
a. State the null and alternative hypothesis for single factor ANOVA to test for any significant
difference in the mean price of gasoline for the three
ands XXXXXXXXXXmarks)
. State the decision rule at 5% significance level XXXXXXXXXXmarks)
c. Calculate the test statistic XXXXXXXXXXmarks)
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d. Based on the calculated test statistics decide whether any significant difference in the mean
price of gasoline for three bands XXXXXXXXXXmarks)
Note: No excel ANOVA output allowed. Students need to show all the steps in calculations.
Question 5: Week 11 Question 3, (7 Marks)
Dex Research Limited conducted a research to investigate consumer characteristics that can be used to
predict the amount charged by credit card users. The following multiple regression output is based on a
data collected by this research company on annual income, household size and annual credit card
charges for a sample if 50 consumers.
Regression Statistics
Multiple R 0.9086
R Square A
Adjusted R Square 0.8181
Standard E
or XXXXXXXXXX
Observations B
ANOVA
df SS MS F Significance F
Regression 2 D E G 1.50876E-18
Residual C XXXXXXXXXXF
Total XXXXXXXXXX
Coefficients Standard E
or t Stat P-value
Intercept XXXXXXXXXX XXXXXXXXXX28664E-08
Income ($1000s XXXXXXXXXXH 7.68206E-11
Household Size XXXXXXXXXX XXXXXXXXXX12342E-14
a. Complete the missing entries from A to H in this output XXXXXXXXXXmarks)
. Estimate the annual credit card charges for a three-person household with an annual income
of $40, XXXXXXXXXX marks)
c. Did the estimated regression equation provide a good fit to the data? Explain XXXXXXXXXXmark)
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Question 6 : Week 12 Question 2, (7 Marks)
Amex PLC has gathered following information on the sales of face mask from April 2020 to
September 2020.
Month Sales ($)
April 17,000
May 18,000
June 19,500
July 22,000
August 21,000
September 23,000
You are required to;
a. Using linear trend equation forecast the sales of face masks for October 2020.
(5 marks)
. Calculate the forecasted sales difference if you use 3-period weighted moving average
designed with the following weights: July 0.2, August 0.3 and September 0.5.
XXXXXXXXXXmarks)
Note: You need to show all the steps in your calculation. No excel files will be graded.
FORMULA SHEET
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K = XXXXXXXXXXlog10 n
Summary Measures (n – sample size; N – Population size)
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∑ ??
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[(∑ ??
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(∑ ??
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?
[(∑ ??
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2]
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4
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?
µ
?? =
?
�̅�
Location of the pth percentile:
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100
(?+1)
IQR = Q3 – Q1
Expected value of a discrete random variable
?(?) = ? = ∑ ? ∗ ?(?)
Variance of a discrete random variable
???(?) = ∑(? − ?)2 ?(?)
Z and t formulas:
? =
?−?
?
? =
�̅�−?
?
√?
? =
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√
??
?
? =
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?
√?
Confidence intervals
Mean:
�̅� ± ??/2