Description

Assessment Task Ã¢â‚¬â€œ Tutorial Questions

Unit Code: HI6007

Unit Name: Statistics for Business Decisions

Assignment: Tutorial Questions Assignment

Due: week 13 (23rd of Feb 2021)

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.

2.

3.

4.

5.

6.

7.

8.

9.

Understand appropriate business research methodologies and how to apply them

to support decision-making process.

Understand various qualitative and quantitative research methodologies and

techniques.

Explain how statistical techniques can solve business problems;

Identify and evaluate valid statistical techniques in a given scenario to solve

business problems;

Explain and justify the results of a statistical analysis in the context of critical

reasoning for a business problem solving

Apply statistical knowledge to summarize data graphically and statistically, either

manually or via a computer package;

Justify and interpret statistical/analytical scenarios that best fits business solution;

Explain and justify value and limitations of the statistical techniques to business

decision making and;

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.

The questions to be answered are;

Question 1

(7 marks)

a. With your own words, using relevant examples briefly define types of probability assigning

methods

(3 marks)

b. Transport trade association conducted a survey of their members to determine what they felt

were the important issues to be discussed with the management. The survey results showed

that 74% felt that the job security was the important issue, while 65% felt that salary

increment was an important issue. Of those who felt salary increment was an important issue,

60% also felt that job security was an important issue.

i.

What percentage of the members felt that both job security and salary increment

were important?

(2 marks)

ii.

What percentage of the members felt that at least one of these two issues was

important?

(2 marks)

Question 2

(7 marks)

Annual food consumption survey shows that number of instant food meals consumed per month by

university students is normally distributed with a mean of 10 and a standard deviation of 3.

a. Calculate the proportion of students consume more than 12 instant meals per month?

b. Estimate the probability that in a random sample of 25 studentsÃ¢â‚¬â„¢ more than 275

instant meals are consumed.

Question 3

(11 marks)

D Dax limited installed a new safety equipment in order to reduce the number of person hours lost as

a result of industrial accident. In a test to of the effectiveness of the equipment, a random sample of

50 departments was chosen. The number of person- hours lost in the month prior to and the month

after the installation of the safety equipment was recorded. The percentage change was calculated

and recorded. Assume that the population standard deviation is 5 and sample mean is -1.2. Can we

infer at the 10% significance level that the new safety equipment is effective?

You are required to

a.

b.

c.

d.

e.

Formulate hypotheses

Decide the suitable test statistics and justify your selection.

Calculate the value of the relevant test statistics and identify the P value

Based on the test statistics in part (III), decide the decision criteria.

Make the final conclusion based on the analysis.

(3 marks)

(1 mark)

(3 marks)

(2 marks)

(2 marks)

Question 4

(11 marks)

The table below shows data on research to examine the perception of business ethics among 3 groups

of employees (higher score indicates higher ethical values).

A

6

5

4

5

6

4

5

4

6

5

B

5

5

4

4

5

4

5

6

5

6

C

6

7

6

5

6

6

6

6

4

5

a. State the null and alternative hypothesis for single factor ANOVA to test for any significant

difference in the perception among three groups.

(1 marks)

b. State the decision rule at 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

(7 marks)

Relax mortgage has gathered following data to examine the relationship between housing starts and

mortgage interest rate.

Interest 3.5

rate

Housing 100

starts

3.0

2.8

3.6

2.75

3.4

3.12

2.86

3.02

2.6

3.3

120

150

130

170

135

130

185

127

190

96

You are required to;

i.

ii.

iii.

Derive the regression equation

(3 marks)

Estimate the no of housing starts if mortgage interest rate is 2.5% (2 marks)

Calculate and interpret the correlation between interest rate and no of

housing starts.

(2 marks)

Question 6

(7 marks)

D& T LTD marketing team needed more information about the effectiveness of their 3 main mode of

advertising. To determine which type is the most effective, the manager collected one weekÃ¢â‚¬â„¢s data

from 25 randomly selected stores. For each store, the following variables were recorded:

Weekly gross sales

Weekly expenditure on direct mailing (Direct)

Weekly expenditure on newspaper advertising (Newspaper)

Weekly expenditure on television commercials (Television)

Following is the regression output based on the above-mentioned data.

SUMMARY OUTPUT

Regression Statistics

Multiple R

R Square

Adjusted R Square

Standard Error

Observations

0.442

A

0.080

2.587

25

ANOVA

Df

Regression

Residual

Total

B

21

C

SS

34.1036

D

174.6631

Intercept

Direct

Newspaper

Television

Coefficients

12.31

0.57

3.32

G

Standard

Error

4.70

1.72

1.54

1.96

F

Significance

F

0.1979

Pvalue

0.02

0.74

0.04

0.71

Lower 95%

2.54

-3.01

0.12

-3.34

MS

F

E

6.6933

t Stat

2.62

H

2.16

0.37

a. Complete the missing entries from A to H in this output

b. Assess the independent variables significance at 5% level

c. Does the model is significant at 5% level?

(2 marks)

(3 marks)

(2 marks)

FORMULA SHEET

K = 1 + 3.3 log10 n

Summary Measures (n Ã¢â‚¬â€œ sample size; N Ã¢â‚¬â€œ Population size)

Ã¢Ë†â€˜Ã°Ââ€˜Â

Ã°Ââ€˜â€“=1 Ã°Ââ€˜â€¹Ã°Ââ€˜â€“

Ã°ÂÅ“â€¡=

Ã°Ââ€˜Â

Ã°Ââ€˜Â 2 =

1

Ã°Ââ€˜â€ºÃ¢Ë†â€™1

Ã°ÂÅ“Å½2 =

1

Ã°Ââ€˜Â

Ã¢Ë†â€˜Ã°Ââ€˜â€º

Ã°Ââ€˜â€“=1 Ã°Ââ€˜â€¹Ã°Ââ€˜â€“

Ã°Ââ€˜ÂÃŒâ€š =

Ã°Ââ€˜â€º

Ã¢Ë†â€˜Ã°Ââ€˜â€ºÃ°Ââ€˜â€“=1(Ã°Ââ€˜Â¥Ã°Ââ€˜â€“ Ã¢Ë†â€™ Ã°Ââ€˜Â¥ÃŒâ€¦ )2

1

[(Ã¢Ë†â€˜Ã°Ââ€˜â€ºÃ°Ââ€˜â€“=1 Ã°Ââ€˜Â¥Ã°Ââ€˜â€“2 ) Ã¢Ë†â€™

Ã°Ââ€˜â€ºÃ¢Ë†â€™1

Or Ã°Ââ€˜Â 2 =

Ã°Ââ€˜Â ~

Ã°Ââ€˜â€¹ÃŒâ€¦ =

Ã°Ââ€˜â€¹

Ã°Ââ€˜â€º

Or Ã°Ââ€˜Â 2 =

(Ã¢Ë†â€˜Ã°Ââ€˜â€º

Ã°Ââ€˜â€“=1 Ã°Ââ€˜Â¥Ã°Ââ€˜â€“ )

Ã°Ââ€˜â€¦Ã°Ââ€˜Å½Ã°Ââ€˜â€ºÃ°Ââ€˜â€Ã°Ââ€˜â€™

]

1

Ã°Ââ€˜Â

2

2

[(Ã¢Ë†â€˜Ã°Ââ€˜Â

Ã°Ââ€˜â€“=1 Ã°Ââ€˜Â¥Ã°Ââ€˜â€“ ) Ã¢Ë†â€™ Ã°Ââ€˜â€ºÃ‚Âµ ]

Ã°ÂÂÂ¶Ã°Ââ€˜â€° =

4

[(Ã¢Ë†â€˜Ã°Ââ€˜â€ºÃ°Ââ€˜â€“=1 Ã°Ââ€˜Â¥Ã°Ââ€˜â€“2 ) Ã¢Ë†â€™ Ã°Ââ€˜â€ºÃ°Ââ€˜Â¥ÃŒâ€¦ 2 ]

2

Ã°Ââ€˜â€º

2

2

Ã¢Ë†â€˜Ã°Ââ€˜Â

Ã°Ââ€˜â€“=1(Ã°Ââ€˜Â¥Ã°Ââ€˜â€“ Ã¢Ë†â€™ Ã‚Âµ) Or Ã°ÂÅ“Å½ =

1

Ã°Ââ€˜â€ºÃ¢Ë†â€™1

Ã°ÂÅ“Å½

Ã‚Âµ

Ã°Ââ€˜Â

Ã°Ââ€˜ÂÃ°Ââ€˜Â£ = Ã°Ââ€˜Â¥ÃŒâ€¦

Location of the pth percentile:

Ã°ÂÂÂ¿Ã°Ââ€˜Â=

Ã°Ââ€˜Â

(Ã°Ââ€˜â€º+1)

100

IQR = Q3 Ã¢â‚¬â€œ Q1

Expected value of a discrete random variable

Ã°ÂÂÂ¸(Ã°Ââ€˜Â¥) = Ã°ÂÅ“â€¡ = Ã¢Ë†â€˜ Ã°Ââ€˜Â¥ Ã¢Ë†â€” Ã°Ââ€˜â€œ(Ã°Ââ€˜Â¥)

Variance of a discrete random variable

Ã°Ââ€˜â€°Ã°Ââ€˜Å½Ã°Ââ€˜Å¸(Ã°Ââ€˜Â¥) = Ã¢Ë†â€˜(Ã°Ââ€˜Â¥ Ã¢Ë†â€™ Ã°ÂÅ“â€¡)2 Ã°Ââ€˜â€œ(Ã°Ââ€˜Â¥)

Z and t formulas:

Ã°Ââ€˜Â=

Ã°Ââ€˜Â¥Ã¢Ë†â€™Ã°ÂÅ“â€¡

Ã°ÂÅ“Å½

Ã°Ââ€˜Â=

Ã°Ââ€˜Â¥ÃŒâ€¦ Ã¢Ë†â€™Ã°ÂÅ“â€¡

Ã°ÂÅ“Å½

Ã¢Ë†Å¡Ã°Ââ€˜â€º

Confidence intervals

Mean:

Ã°Ââ€˜Â¥ÃŒâ€¦ Ã‚Â± Ã°Ââ€˜Â§Ã°Ââ€ºÂ¼/2

Ã°ÂÅ“Å½

Ã¢Ë†Å¡Ã°Ââ€˜â€º

Ã°Ââ€˜Â=

Ã°Ââ€˜ÂÃŒâ€šÃ¢Ë†â€™Ã°Ââ€˜Â

Ã°Ââ€˜ÂÃ°Ââ€˜Å¾

Ã¢Ë†Å¡

Ã°Ââ€˜â€º

Ã°Ââ€˜Â¡=

Ã°Ââ€˜Â¥ÃŒâ€¦ Ã¢Ë†â€™Ã°ÂÅ“â€¡

Ã°Ââ€˜Â

Ã¢Ë†Å¡Ã°Ââ€˜â€º

Ã°Ââ€˜Â¥ÃŒâ€¦ Ã‚Â± Ã°Ââ€˜Â¡Ã°Ââ€ºÂ¼/2

Ã°Ââ€˜Â

Ã¢Ë†Å¡Ã°Ââ€˜â€º

Proportion:

Ã°Ââ€˜ÂÃŒâ€š Ã°Ââ€˜Å¾ÃŒâ€š

Ã°Ââ€˜ÂÃŒâ€š Ã‚Â± Ã°Ââ€˜Â§Ã°Ââ€ºÂ¼ Ã¢Ë†Å¡

Ã°Ââ€˜â€º

2

Ã°Ââ€˜â€º=

2

Ã°Ââ€˜Â§Ã°Ââ€ºÂ¼/2

Ã°Ââ€˜ÂÃ°Ââ€˜Å¾

Ã°ÂÂÂµ2

Time Series Regression

Ã°Ââ€˜Â1 =

Ã¢Ë†â€˜Ã°Ââ€˜â€ºÃ°Ââ€˜Â¡=1[(Ã°Ââ€˜Â¡ Ã¢Ë†â€™ Ã°Ââ€˜Â¡)(Ã°Ââ€˜Â¦Ã°Ââ€˜Â¡ Ã¢Ë†â€™ Ã°Ââ€˜Â¦)]

Ã¢Ë†â€˜Ã°Ââ€˜â€ºÃ°Ââ€˜Â¡=1(Ã°Ââ€˜Â¡ Ã¢Ë†â€™ Ã°Ââ€˜Â¡)

2

Ã°Ââ€˜Â0 = Ã°Ââ€˜Å’ Ã¢Ë†â€™ Ã°Ââ€˜Â1 Ã°Ââ€˜Â¡

Ã°Ââ€˜â€¡Ã°Ââ€˜Â¡ = Ã°Ââ€˜Â0 + Ã°Ââ€˜Â1 Ã°Ââ€˜Â¡

ANOVA:

Ã°Ââ€˜â€ Ã°Ââ€˜â€ Ã°Ââ€˜â€¡Ã°Ââ€˜â€¦

MSTR =

Ã°Ââ€˜ËœÃ¢Ë†â€™1

MSE =

Ã°Ââ€˜Ëœ

SSTR = Ã¢Ë†â€˜ Ã°Ââ€˜â€ºÃ°Ââ€˜â€” (Ã°Ââ€˜Â¥ÃŒâ€¦Ã°Ââ€˜â€” Ã¢Ë†â€™ Ã°Ââ€˜Â¥ÃŒÂ¿ )

SSE

Ã°Ââ€˜â€ºÃ°Ââ€˜â€¡ Ã¢Ë†â€™ Ã°Ââ€˜Ëœ

Ã°Ââ€˜Ëœ

2

Ã°Ââ€˜â€”=1

Ã°Ââ€˜â€ºÃ°Ââ€˜â€”

SST = Ã¢Ë†â€˜ Ã¢Ë†â€˜(Ã°Ââ€˜Â¥Ã°Ââ€˜â€“Ã°Ââ€˜â€” Ã¢Ë†â€™ Ã°Ââ€˜Â¥ÃŒÂ¿ )

2

Ã°Ââ€˜â€”=1 Ã°Ââ€˜â€“=1

Ã°Ââ€˜Ëœ

SSE = Ã¢Ë†â€˜(Ã°Ââ€˜â€ºÃ°Ââ€˜â€” Ã¢Ë†â€™ 1)Ã°Ââ€˜Â Ã°Ââ€˜â€” 2

F = MSTR / MSE

Ã°Ââ€˜â€”=1

Simple Linear Regression:

ÃŒâ€šÃ°Ââ€˜Â¦ = Ã°Ââ€˜Â0 + Ã°Ââ€˜Â1 Ã°Ââ€˜Â¥

Ã°Ââ€˜Â1 =

Ã¢Ë†â€˜(Ã°Ââ€˜Â¥Ã°Ââ€˜â€“ Ã¢Ë†â€™ Ã°Ââ€˜Â¥ÃŒâ€¦ )(Ã°Ââ€˜Â¦Ã°Ââ€˜â€“ Ã¢Ë†â€™ Ã°Ââ€˜Â¦ÃŒâ€¦)

Ã¢Ë†â€˜(Ã°Ââ€˜Â¥Ã°Ââ€˜â€“ Ã¢Ë†â€™ Ã°Ââ€˜Â¥ÃŒâ€¦ )2

SSE = Ã¢Ë†â€˜(Ã°Ââ€˜Â¦Ã°Ââ€˜â€“ Ã¢Ë†â€™ Ã°Ââ€˜Â¦ÃŒâ€šÃ°Ââ€˜â€“ )2

SSR= Ã¢Ë†â€˜(Ã°Ââ€˜Â¦ÃŒâ€šÃ°Ââ€˜â€“ Ã¢Ë†â€™ Ã°Ââ€˜Â¦ÃŒâ€¦)2

Coefficient of determination

Ã°Ââ€˜Â0 = Ã°Ââ€˜Â¦ÃŒâ€¦ Ã¢Ë†â€™ Ã°Ââ€˜Â1 Ã°Ââ€˜Â¥ÃŒâ€¦

SST

=

SSR

SST = Ã¢Ë†â€˜(Ã°Ââ€˜Â¦Ã°Ââ€˜â€“ Ã¢Ë†â€™ Ã°Ââ€˜Â¦ÃŒâ€¦)2

+

SSE

R2= SSR/SST

Correlation coefficient

Ã°Ââ€˜Å¸=

Ã¢Ë†â€˜(Ã°Ââ€˜Â¥Ã¢Ë†â€™ Ã°Ââ€˜Â¥ÃŒâ€¦ )(Ã°Ââ€˜Â¦Ã¢Ë†â€™ Ã°Ââ€˜Â¦)

Ã°Ââ€˜Å¸=

or

Ã¢Ë†Å¡(Ã¢Ë†â€˜(Ã°Ââ€˜Â¥Ã¢Ë†â€™ Ã°Ââ€˜Â¥)2 )(Ã¢Ë†â€˜(Ã°Ââ€˜Â¦Ã¢Ë†â€™ Ã°Ââ€˜Â¦)2 )

Ã¢Ë†â€˜ Ã°Ââ€˜â€¹Ã°Ââ€˜Å’Ã¢Ë†â€™

Ã¢Ë†Å¡(Ã¢Ë†â€˜ Ã°Ââ€˜â€¹ 2 Ã¢Ë†â€™

Ã¢Ë†â€˜Ã°Ââ€˜â€¹ Ã¢Ë†â€˜Ã°Ââ€˜Å’

Ã°Ââ€˜Â

(Ã¢Ë†â€˜ Ã°Ââ€˜â€¹)2

(Ã¢Ë†â€˜ Ã°Ââ€˜Å’)2

)(Ã¢Ë†â€˜ Ã°Ââ€˜Å’ 2 Ã¢Ë†â€™

)

Ã°Ââ€˜Â

Ã°Ââ€˜Â

R2 = (Ã°Ââ€˜Å¸Ã°Ââ€˜Â¥Ã°Ââ€˜Â¦ )2

Ã°Ââ€˜Å¸Ã°Ââ€˜Â¥Ã°Ââ€˜Â¦ = (sign of Ã°Ââ€˜Â1 )Ã¢Ë†Å¡Coefficient of Determination

Testing for Significance

2

s = MSE = SSE/(n

Ã°Ââ€˜Â Ã°Ââ€˜Â1 =

SSE

s = Ã¢Ë†Å¡MSE = Ã¢Ë†Å¡Ã°Ââ€˜â€ºÃ¢Ë†â€™2

2)

Ã°Ââ€˜Â

Ã¢Ë†Å¡Ã¢Ë†â€˜(Ã°Ââ€˜Â¥Ã°Ââ€˜â€“ Ã¢Ë†â€™

Ã°Ââ€˜Â¡=

Ã°Ââ€˜Â¥ÃŒâ€¦ )2

MSR = SSR/k-1

MSE = SSE/n-k

Confidence Interval for ÃŽÂ²1

Ã°Ââ€˜Â1 Ã‚Â± Ã°Ââ€˜Â¡Ã°Ââ€ºÂ¼/2 Ã°Ââ€˜Â Ã°Ââ€˜Â1

Multiple Regression:

y = Ã¯ÂÂ¢ + Ã¯ÂÂ¢ x + Ã¯ÂÂ¢ x +. . . + Ã¯ÂÂ¢ x + Ã¯ÂÂ¥

0

1 1

2 2

p p

Ã°Ââ€˜Â¦ÃŒâ€š = b + b x + b x + . . . + b x

0

1 1

2 2

Ã°Ââ€˜â€¦Ã°Ââ€˜Å½ 2 = 1 Ã¢Ë†â€™ (1 Ã¢Ë†â€™ Ã°Ââ€˜â€¦ 2 )

R2 = SSR/SST

Ã°Ââ€˜Â1

Ã°Ââ€˜Â Ã°Ââ€˜Â1

p p

Ã°Ââ€˜â€ºÃ¢Ë†â€™1

Ã°Ââ€˜â€ºÃ¢Ë†â€™Ã°Ââ€˜ÂÃ¢Ë†â€™1

F = MSTR / MSE

F distribution

Submission Directions:

The 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.

Academic Integrity

Holmes Institute is committed to ensuring and upholding Academic Integrity, as Academic Integrity is

integral to maintaining academic quality and the reputation of HolmesÃ¢â‚¬â„¢ graduates. Accordingly, all

assessment tasks need to comply with academic integrity guidelines. Table 1 identifies the six

categories of Academic Integrity breaches. If you have any questions about Academic Integrity issues

related to your assessment tasks, please consult your lecturer or tutor for relevant referencing

guidelines and support resources. Many of these resources can also be found through the Study Skills

link on Blackboard.

Academic Integrity breaches are a serious offence 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.

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 authorised.

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 offence.

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.

Source: INQAAHE, 2020

If any words or ideas used 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 InstituteÃ¢â‚¬â„¢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.

Further Information:

For further information and additional learning resources please refer to your Discussion Board for

the unit.

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