 # HI6007 STATISTICS FOR BUSINESS TUTORIAL

## Assessment Task – Tutorial Questions

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### 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 the 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 business problems;

5.     Explain  and  justify  the  results  of statistical  analysis  in  the  context  of  critical reasoning 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 fit 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 questions for weeks 1 to 11 inclusive and submit these answers in a single document.

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.

42            66            67            71            78            62            61            76            71            67

61            64            61            54            83            63            68            69            81            53

Based on the information given you are required to

i.       Compute the mean, median, and mode.                                                                (3 marks) ii.       Compute the first and third quartiles.                                                                     (1 mark) iii.       Compute and interpret the 90th  percentile.                                                            (1 mark)

b.    In your own word, explain what is inferential statistics with relevant examples.

(2 marks)

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.

Age Group

Applied to more than 1 university

Yes                                    No

23 and under                  207                                   201

24-26                               299                                   379

27-30                               185                                   268

31-35                               66                                     193

36 and over                    51                                     169

i.       Prepare a joint probability table                                                                               (1 mark)

ii.        Given that a student applied to more than 1 university, what is the probability that the student is 24-26 years old.                                                                                  (1 mark)

iii.       Is the number of universities applied to independent of student age? Explain

(2 marks)

b.    Assume, North Origano, is a country with the 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

i.       Compute the expected value and variance of x.                                        (3 marks)

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Question 3: Week 8 Question 3, (11 Marks)

According to the  Annual Survey of Drug 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).                                                                                                                      (3 marks)

II.       Decide the suitable test statistics and justify your selection.                                              (1 mark) III.       Calculate the value of the relevant test statistics and identify the P-value                    (3 marks) 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.                                                               (3 marks)

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 the gasoline service station for three major brands of gasoline (A, B and C) located in 10 metropolitan areas across the country X.

A                       B                          C

3.77                  3.83                     3.78

3.72                  3.83                     3.87

3.87                  3.85                     3.89

3.76                  3.77                     3.79

3.83                  3.84                     3.87

3.85                  3.84                     3.87

3.93                  4.04                     3.99

3.79                  3.78                     3.79

3.78                  3.84                     3.79

3.81                  3.84                     3.86

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 brands.                                        (1 marks)

b.    State the decision rule at a 5% significance level.                                                                  (2 marks)

c.    Calculate the test statistic.                                                                                                      (6 marks)

d.    Based on the calculated test statistics decide whether any significant difference in the mean price of gasoline for three bands.                                                                                          (2 marks)

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 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 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 Error                 398.0910

Observations                                  B

ANOVA

df                    SS                                 MS                      F                   Significance F

Regression                 2                                  D                        E                        G                          1.50876E-18

Residual                      C                     7448393.148                F Total                            49                   42699148.82

Coefficients  Standard Error        t Stat               P-value

Intercept                         1304.9048           197.6548            6.6019     3.28664E-08

Income (\$1000s)                33.1330                3.9679           H                7.68206E-11

Household Size                356.2959             33.2009     10.7315          3.12342E-14

a.    Complete the missing entries from A to H in this output                                                  (4 marks) b.    Estimate the annual credit card charges for a three-person household with an annual income of \$40,000.                                                                                                                                 (2 marks)

c.    Did the estimated regression equation provide a good fit to the data? Explain            (1 mark)

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Question 6: Week 12 Question 2, (7 Marks)

Amex PLC has gathered the following information on the sales of face mask from April 2020 to

September 2020.

You are required to;

Month                           Sales (\$)

April                               17,000

May                                18,000

June                                19,500

July                                 22,000

August                           21,000

September                    23,000

a.    Using linear trend equation forecast the sales of face masks for October 2020.

(5 marks)

b.    Calculate the forecasted sales difference if you use a 3-period weighted moving average designed with the following weights: July 0.2, August 0.3, and September 0.5.

(2 marks)

Note: You need to show all the steps in your calculation. No excel files will be graded.

FORMULA SHEET

K = 1 + 3.3 log10  n

Summary Measures    (n – sample size; N – Population size)

𝜇 =

∑𝑁      � �

𝑁

�̅ =

∑𝑛       � �

𝑛

� =   �

𝑛

�2  =      1     ∑𝑛

(�  − �)2

Or  �2  =      1     [(∑𝑛

�2) − 𝑛�2]

𝑛−1

�=1      �

𝑛−1

�=1    �

𝑛             2

Or �2  =      1     [(∑𝑛

�2) −  ( ∑� =1  � � )   ]

𝑛−1

�=1    �                     𝑛

𝜎2  =   1  ∑𝑁

(�  − µ)2  Or  𝜎2  =   1  [(∑𝑁

�2) − 𝑛µ2]

𝑁

�~  𝑅 �𝑛𝑔𝑒

4

�=1      �

𝑁

�𝑉 =  𝜎

µ

�=1

�𝑣 =  �

Location of the pth  percentile:

𝑝

(𝑛+1)

100

IQR = Q3  – Q1

The expected value of a discrete random variable

𝐸(�) = 𝜇 = ∑ � ∗ 𝑓(�)

The variance of a discrete random variable

𝑉��(�) = ∑(� − 𝜇)2 𝑓(�)

Z and formulas:

� =  � − 𝜇

𝜎

� − 𝜇

𝜎

√𝑛

� = 𝑝̂− 𝑝

��

√ 𝑛

� − 𝜇

𝑠

√𝑛

Confidence intervals

Mean:

� ± �𝛼/2

𝜎

√𝑛

� ± �𝛼/2

√𝑛

Proportion:

� �̂

�  ±  � 𝛼 √

2        𝑛

𝑛 =

2

𝛼/2

�2

Time Series Regression

∑ 𝑛      [ ( �  −   � ) ( ��   −   � ) ]

�1  =

∑𝑛     (� −  �)2

�0  =  � −  �1�

��  =  �0  +  �1�

ANOVA:

MSTR =

����

𝑘 − 1

MSE =

SSE

𝑛𝑇  − 𝑘

�                                                                           �      𝑛�

2                                                                                2

SSTR = ∑ 𝑛�(��  − �)

�=1

SSE =  ∑(𝑛�  − 1)��2

�=1

Simple Linear Regression:

̂� = �0  + �1�

∑( ��   −  � ) ( ��   −  �̅ )

SST = ∑ ∑(���  − �)

�=1  �=1

= MSTR / MSE

�0  = �̅ − �1�

�1  =

∑(��

− �)2

SST    =    SSR    +    SSE

SSE = ∑(��  − �̂�)2                                                  SST = ∑(��  − �̅)2

SSR= ∑(�̂�  − �̅)2

Coefficient of determination

R2= SSR/SST

Correlation coefficient

∑(�− �)(�− �)

∑ ��−

∑ �  ∑ �

� =

or

� =                                                 𝑁

√(∑(�− �)2)(∑(�− �)2)

√(∑ �2−  ( ∑  �) 2 )(∑ �2−  ( ∑  � ) 2

𝑁                                 𝑁

R= (��� )2

���  = (sign of �1)√Coefficient of Determination

Testing for Significance

s    = MSE = SSE/(n     2)                     s = √MSE = √ SSE

𝑛−2

��1   =

√∑(��  − �)2

�1

� =

��1

= MSTR / MSE

MSR = SSR/k-1              MSE = SSE/n-k

Confidence Interval for β1

�1  ± �𝛼/2��1

Multiple Regression:

= 

+  x

+  x

+ . . . +  x  + 

0          1   1          2   2                       p   p

�̂ = b

b x

b x

+ . . . + b x

0         1   1

2   2                       p   p

𝑛 − 1

��2  = 1 −  (1 − �2)

𝑛 − � − 1

R2  = SSR/SST

\distribution

Submission Directions:

An assignment will be submitted via Blackboard.  Each student will be permitted only ONE submission to Blackboard.  You need to ensure that the document submitted is the correct one.

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Academic Integrity breaches are a serious offense punishable by penalties that may range from deduction of marks, failure of the assessment task or unit involved, suspension of course enrolment, or cancellation of course enrolment.

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Table 1: Six categories of Academic Integrity breaches

Plagiarism                                Reproducing the work of someone else without attribution. When a student submits their own work on multiple occasions this is known as self-plagiarism.

Collusion                                  Working with one or more other individuals to complete an assignment, in a way that is not authorized.

Copying                                    Reproducing and submitting the work of another student, with or without their knowledge. If a student fails to take reasonable precautions to prevent their own original work from being copied, this may also be considered an offense.

Impersonation                       Falsely presenting oneself or engaging someone else to present as oneself, in an in-person examination.

Contract cheating                  Contracting a third party to complete an assessment task, generally in exchange for money or other manner of payment.

Data fabrication and falsification

Manipulating or inventing data with the intent of supporting false conclusions, including manipulating images.

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Source: INQAAHE, 2020

If any words or ideas used in the assignment submission do not represent your original words or ideas, you must cite all relevant sources and make clear the extent to which such sources were used.

In addition, written assignments that are similar or identical to those of another student is also a violation of the Holmes  Institute’s  Academic  Conduct and  Integrity policy.  The consequence for a violation of this policy can incur a range of penalties varying from a 50% penalty through suspension of enrolment.   The penalty would be dependent on the extent of academic misconduct and your history of academic misconduct issues.

All assessments will be automatically submitted to SelfAssign to assess their originality.