Student Number: (enter on the line below)

Student Name: (enter on the line below)

HI6007

Statistics for Business Decisions

Final AssIGNMENt

Trimester 1, 2021

Assessment Weight: 50 total marks

Instructions:

All questions must be answered by using the answer boxes provided in this paper.

Completed answers must be submitted to Blackboard by the published due date and time.

Submission instructions are at the end of this paper.

Purpose:

This assessment consists of six (6) questions and is designed to assess your level of knowledge of the key topics covered in this unit

Question 1 ( 7 marks)

Holmes institute Students evaluation of the course they follow, askes following questions from students. Identify the type of data and measurement scale for each with relevant justifications.

How many interactive tutorials did you attend in this semester?

What was your group assignment grade (HD, D, C, P, F)?

Rate the lecturer (very effective, effective, not too effective and not at all effective)

Which campus you are registered in (Melbourne, Sydney, Brisbane or Gold coast)

(2 marks)

ANSWER: ** Answer box will enlarge as you type

An investor recorded the following annual returns of one of his investments. You are required to calculate and comment on;

Mean return.

Variance and standard deviation of the return.

Geometric return.

Year 2016 2017 2018 2019 2020

Return 15% 17% 19% 10% -5%

(5 marks)

ANSWER: ** Answer box will enlarge as you type

Question 2 (11 marks)

Nature lovers’ association of Australia, launched a campaign to encourage paper less communication and/or recycling of used papers to save the trees to reduce global warming. Hence, many small businesses have scaled up their business such as new forms of online document exchanges and collecting used papers and cardboards from households and companies.

Abita Recycling Ltd is one such company which is operates in Melbourne. The financial analysist of the company has estimated that the firm would make a profit if the mean weekly collection of papers and cardboards from each household exceeded 1KG. To examine the feasibility of a recycling plant, a random sample of 100 households was selected and sample mean and standard deviations are 1.1KG and 0.35KG respectively.

Following the 6-step process of hypothesis testing, you are required to examine do this information provide sufficient evidence at 99% confidence to allow the analyst to conclude that a recycling plant would be profitable?

ANSWER:

Question 3 (11 marks)

Edex limited is a renowned agricultural chemical manufacturer in Australia. They conduct many research and development in the field of Agri and Horticulture. Company wanted to examine the effect of temperature on farming of their selected range of products.

Company has produced following results based on their data gathering.

15° C 35 24 36 39 32

25° C 30 31 34 23 27

35° C 23 28 28 30 31

You are required to answer following questions;

State the null and alternative hypothesis for single factor ANOVA to test for any significant difference in the perception among three groups. (1 marks)

ANSWER:

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

ANSWER:

Calculate the test statistic. (6 marks)

ANSWER:

Based on the calculated test statistics, decide whether there are any significant differences between the yield based on the given temperature levels. (2 marks)

ANSWER:

Note: No excel ANOVA output allowed in question3. Students need to show all the steps in calculations.

Question 4 (7 marks)

Melbourne Uni Lodge has decided to provide cup of cold or hot drinks for their tenants to attract them after the Covid pandemic. They have determined that mean number of cups of drinks per day is 2.00 with the standard deviation of 0.6. There will be 125 new tenants in the upcoming months.

What is the probability that the new tenants will consume more than 240 cups of drinks per day?

ANSWER:

Question 5 (7 marks)

Yummy Lunch Restaurant needs to decide the most profitable location for their business expansion. Marketing manager plans to use a multiple regression model to achieve their target. His model considers yearly revenue as the dependent variable. He found that number of people within 2KM (People), Mean household income(income), no of competitors and price as explanatory variables of company yearly revenue.

The following is the descriptive statistics and regression output from Excel.

Revenue People Income Competitors Price

Mean 343965.68 5970.26 41522.96 2.8 5.68

Standard Error 5307.89863 139.0845281 582.1376385 0.142857 0.051030203

Median 345166.5 6032 41339.5 3 5.75

Mode #N/A 5917 #N/A 3 6

Standard Deviation 37532.51115 983.47613 4116.334718 1.010153 0.360838027

Sample Variance 1408689393 967225.2984 16944211.51 1.020408 0.130204082

Sum 17198284 298513 2076148 140 284

Count 50 50 50 50 50

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.77

R Square A

Adjusted R Square B

Standard Error 25139.79

Observations 50.00

ANOVA

df SS MS F Significance F

Regression C 40585376295 F H 3.0831E-08

Residual D 28440403984 G

Total E 69025780279

Coefficients Standard Error t Stat P-value

Intercept -68363.1524 78524.7251 -0.8706 0.3886

People 6.4394 3.7051 I 0.0891

Income 7.2723 0.9358 J 0.0000

Competitors -6709.4320 3818.5426 K 0.0857

Price 15968.7648 10219.0263 L 0.1251

You are required to;

Complete the missing entries from A to L in this output (2 marks)

ANSWER:

Derive the regression model (1 mark)

ANSWER:

What does the standard error of estimate tell you about the model? (1 mark)

ANSWER:

Assess the independent variables significance at 5% level (develop hypothesis if necessary in the analysis)? (3 marks)

ANSWER:

Question 6 (7 marks)

Anita Limited has shared their annual sales revenue over the last 6 financial years from 2015 to 2020.

Year Sales ($ 000)

2015 4500

2016 5100

2017 4900

2018 5400

2019 5670

2020 6000

You are required to;

Using linear trend equation forecast the sales revenue of Anita Limited for 2021. (5 marks)

ANSWER:

Calculate the forecasted sales difference if you use 3-period weighted moving average designed with the following weights: 2018 (0.1), 2019 (0.3) and 2020(0.6). (2 marks)

ANSWER:

Note: See the formula sheet on the next page.

FORMULA SHEET

K = 1 + 3.3 log10 n

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

µ= (?_(i=1)^N¦X_i )/N X ¯= (?_(i=1)^n¦X_i )/n p ^= X/n

s^2= 1/(n-1) ?_(i=1)^n¦(x_i-x ¯ )^2 Or s^2= 1/(n-1) [(?_(i=1)^n¦x_i^2 )-nx ¯^2 ]

Or s^2= 1/(n-1) [(?_(i=1)^n¦x_i^2 )-(?_(i=1)^n¦x_i )^2/n]

s^2= 1/N ?_(i=1)^N¦(x_i-µ)^2 Or s^2= 1/N [(?_(i=1)^N¦x_i^2 )-nµ^2 ]

s~Range/4 CV=s/µ cv=s/x ¯

Location of the pth percentile:

L_(p= p/100(n+1))

IQR = Q3 – Q1

Expected value of a discrete random variable

E(x)=µ=?¦?x*f(x)?

Variance of a discrete random variable

Var(x)=?¦(x-µ)^2 f(x)

Z and t formulas:

Z=(x-µ)/s Z=(x ¯-µ)/(s/vn) Z=(p ^-p)/v(pq/n) t=(x ¯-µ)/(s/vn)

Confidence intervals

Mean:

x ¯±t_(a/2) s/vn

Proportion:

p ^ ± z_(a/2) v((p ^ q ^)/n)

n= (z_(a/2)^2 p q)/B^2

Time Series Regression

b_1= (?_(t=1)^n¦[(t- ¯t)(y_t- ¯y)] )/(?_(t=1)^n¦(t- ¯t)^2 )

b_0= ¯Y- b_1 ¯t

T_t= b_0+ b_1 t

ANOVA:

SSE= ?_(j=1)^k¦?(n_j-1) ?s_j?^2 ?

Simple Linear Regression:

SSE = ?¦(y_i-y ^_i )^2 SST = ?¦(y_i-y ¯ )^2

SSR= ?¦(y ^_i-y ¯ )^2

Coefficient of determination

Correlation coefficient

r= (?¦(x- x ¯ )(y- ¯y) )/v((?¦(x- ¯x)^2 )(?¦(y- ¯y)^2 ) ) or r= (?¦XY- (?¦?X ?¦Y?)/N)/v((?¦X^2 - (?¦X)^2/N)(?¦Y^2 - (?¦Y)^2/N) )

R2 =(?r_(xy ))?^2

Testing for Significance

Confidence Interval for ß1

b_1±t_(a/2) s_(b_1 )

Multiple Regression:

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 Holmes’ 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 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 Self-Assign to assess their originality.

Further Information:

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

END OF TUTORIAL ASSIGNMENT

Submission instructions:

Save submission with your STUDENT ID NUMBER and UNIT CODE e.g. EMV54897 HI6007

Submission must be in MICROSOFT WORD FORMAT ONLY

Upload your submission to the appropriate link on Blackboard

Only one submission is accepted. Please ensure your submission is the correct document.

All submissions are automatically passed through SafeAssign to assess academic integrity.

Student Name: (enter on the line below)

HI6007

Statistics for Business Decisions

Final AssIGNMENt

Trimester 1, 2021

Assessment Weight: 50 total marks

Instructions:

All questions must be answered by using the answer boxes provided in this paper.

Completed answers must be submitted to Blackboard by the published due date and time.

Submission instructions are at the end of this paper.

Purpose:

This assessment consists of six (6) questions and is designed to assess your level of knowledge of the key topics covered in this unit

Question 1 ( 7 marks)

Holmes institute Students evaluation of the course they follow, askes following questions from students. Identify the type of data and measurement scale for each with relevant justifications.

How many interactive tutorials did you attend in this semester?

What was your group assignment grade (HD, D, C, P, F)?

Rate the lecturer (very effective, effective, not too effective and not at all effective)

Which campus you are registered in (Melbourne, Sydney, Brisbane or Gold coast)

(2 marks)

ANSWER: ** Answer box will enlarge as you type

An investor recorded the following annual returns of one of his investments. You are required to calculate and comment on;

Mean return.

Variance and standard deviation of the return.

Geometric return.

Year 2016 2017 2018 2019 2020

Return 15% 17% 19% 10% -5%

(5 marks)

ANSWER: ** Answer box will enlarge as you type

Question 2 (11 marks)

Nature lovers’ association of Australia, launched a campaign to encourage paper less communication and/or recycling of used papers to save the trees to reduce global warming. Hence, many small businesses have scaled up their business such as new forms of online document exchanges and collecting used papers and cardboards from households and companies.

Abita Recycling Ltd is one such company which is operates in Melbourne. The financial analysist of the company has estimated that the firm would make a profit if the mean weekly collection of papers and cardboards from each household exceeded 1KG. To examine the feasibility of a recycling plant, a random sample of 100 households was selected and sample mean and standard deviations are 1.1KG and 0.35KG respectively.

Following the 6-step process of hypothesis testing, you are required to examine do this information provide sufficient evidence at 99% confidence to allow the analyst to conclude that a recycling plant would be profitable?

ANSWER:

Question 3 (11 marks)

Edex limited is a renowned agricultural chemical manufacturer in Australia. They conduct many research and development in the field of Agri and Horticulture. Company wanted to examine the effect of temperature on farming of their selected range of products.

Company has produced following results based on their data gathering.

15° C 35 24 36 39 32

25° C 30 31 34 23 27

35° C 23 28 28 30 31

You are required to answer following questions;

State the null and alternative hypothesis for single factor ANOVA to test for any significant difference in the perception among three groups. (1 marks)

ANSWER:

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

ANSWER:

Calculate the test statistic. (6 marks)

ANSWER:

Based on the calculated test statistics, decide whether there are any significant differences between the yield based on the given temperature levels. (2 marks)

ANSWER:

Note: No excel ANOVA output allowed in question3. Students need to show all the steps in calculations.

Question 4 (7 marks)

Melbourne Uni Lodge has decided to provide cup of cold or hot drinks for their tenants to attract them after the Covid pandemic. They have determined that mean number of cups of drinks per day is 2.00 with the standard deviation of 0.6. There will be 125 new tenants in the upcoming months.

What is the probability that the new tenants will consume more than 240 cups of drinks per day?

ANSWER:

Question 5 (7 marks)

Yummy Lunch Restaurant needs to decide the most profitable location for their business expansion. Marketing manager plans to use a multiple regression model to achieve their target. His model considers yearly revenue as the dependent variable. He found that number of people within 2KM (People), Mean household income(income), no of competitors and price as explanatory variables of company yearly revenue.

The following is the descriptive statistics and regression output from Excel.

Revenue People Income Competitors Price

Mean 343965.68 5970.26 41522.96 2.8 5.68

Standard Error 5307.89863 139.0845281 582.1376385 0.142857 0.051030203

Median 345166.5 6032 41339.5 3 5.75

Mode #N/A 5917 #N/A 3 6

Standard Deviation 37532.51115 983.47613 4116.334718 1.010153 0.360838027

Sample Variance 1408689393 967225.2984 16944211.51 1.020408 0.130204082

Sum 17198284 298513 2076148 140 284

Count 50 50 50 50 50

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.77

R Square A

Adjusted R Square B

Standard Error 25139.79

Observations 50.00

ANOVA

df SS MS F Significance F

Regression C 40585376295 F H 3.0831E-08

Residual D 28440403984 G

Total E 69025780279

Coefficients Standard Error t Stat P-value

Intercept -68363.1524 78524.7251 -0.8706 0.3886

People 6.4394 3.7051 I 0.0891

Income 7.2723 0.9358 J 0.0000

Competitors -6709.4320 3818.5426 K 0.0857

Price 15968.7648 10219.0263 L 0.1251

You are required to;

Complete the missing entries from A to L in this output (2 marks)

ANSWER:

Derive the regression model (1 mark)

ANSWER:

What does the standard error of estimate tell you about the model? (1 mark)

ANSWER:

Assess the independent variables significance at 5% level (develop hypothesis if necessary in the analysis)? (3 marks)

ANSWER:

Question 6 (7 marks)

Anita Limited has shared their annual sales revenue over the last 6 financial years from 2015 to 2020.

Year Sales ($ 000)

2015 4500

2016 5100

2017 4900

2018 5400

2019 5670

2020 6000

You are required to;

Using linear trend equation forecast the sales revenue of Anita Limited for 2021. (5 marks)

ANSWER:

Calculate the forecasted sales difference if you use 3-period weighted moving average designed with the following weights: 2018 (0.1), 2019 (0.3) and 2020(0.6). (2 marks)

ANSWER:

Note: See the formula sheet on the next page.

FORMULA SHEET

K = 1 + 3.3 log10 n

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

µ= (?_(i=1)^N¦X_i )/N X ¯= (?_(i=1)^n¦X_i )/n p ^= X/n

s^2= 1/(n-1) ?_(i=1)^n¦(x_i-x ¯ )^2 Or s^2= 1/(n-1) [(?_(i=1)^n¦x_i^2 )-nx ¯^2 ]

Or s^2= 1/(n-1) [(?_(i=1)^n¦x_i^2 )-(?_(i=1)^n¦x_i )^2/n]

s^2= 1/N ?_(i=1)^N¦(x_i-µ)^2 Or s^2= 1/N [(?_(i=1)^N¦x_i^2 )-nµ^2 ]

s~Range/4 CV=s/µ cv=s/x ¯

Location of the pth percentile:

L_(p= p/100(n+1))

IQR = Q3 – Q1

Expected value of a discrete random variable

E(x)=µ=?¦?x*f(x)?

Variance of a discrete random variable

Var(x)=?¦(x-µ)^2 f(x)

Z and t formulas:

Z=(x-µ)/s Z=(x ¯-µ)/(s/vn) Z=(p ^-p)/v(pq/n) t=(x ¯-µ)/(s/vn)

Confidence intervals

Mean:

x ¯±t_(a/2) s/vn

Proportion:

p ^ ± z_(a/2) v((p ^ q ^)/n)

n= (z_(a/2)^2 p q)/B^2

Time Series Regression

b_1= (?_(t=1)^n¦[(t- ¯t)(y_t- ¯y)] )/(?_(t=1)^n¦(t- ¯t)^2 )

b_0= ¯Y- b_1 ¯t

T_t= b_0+ b_1 t

ANOVA:

SSE= ?_(j=1)^k¦?(n_j-1) ?s_j?^2 ?

Simple Linear Regression:

SSE = ?¦(y_i-y ^_i )^2 SST = ?¦(y_i-y ¯ )^2

SSR= ?¦(y ^_i-y ¯ )^2

Coefficient of determination

Correlation coefficient

r= (?¦(x- x ¯ )(y- ¯y) )/v((?¦(x- ¯x)^2 )(?¦(y- ¯y)^2 ) ) or r= (?¦XY- (?¦?X ?¦Y?)/N)/v((?¦X^2 - (?¦X)^2/N)(?¦Y^2 - (?¦Y)^2/N) )

R2 =(?r_(xy ))?^2

Testing for Significance

Confidence Interval for ß1

b_1±t_(a/2) s_(b_1 )

Multiple Regression:

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 Holmes’ 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 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 Self-Assign to assess their originality.

Further Information:

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

END OF TUTORIAL ASSIGNMENT

Submission instructions:

Save submission with your STUDENT ID NUMBER and UNIT CODE e.g. EMV54897 HI6007

Submission must be in MICROSOFT WORD FORMAT ONLY

Upload your submission to the appropriate link on Blackboard

Only one submission is accepted. Please ensure your submission is the correct document.

All submissions are automatically passed through SafeAssign to assess academic integrity.

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