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Assessment Task – Tutorial Questions

Unit Code: HI6007

Unit Name: Statistics for Business Decisions

Assignment: Tutorial Questions 2

Due: 11:59PM 19 June 2020

Weighting: 25%

Purpose: This assignment is designed to assess your level of knowledge of the key topics covered in

this unit

Unit Learning Outcomes Assessed:

1. Students are able to apply appropriate business research methodologies to support

decision-making process.

2. Students are able to identify and apply valid statistical techniques in a given scenario to

solve business problems.

3. Students are able to justify and interpret the results of a statistical analysis in the context

of critical reasoning for a business problem solving.

4. Students are able to apply statistical knowledge to summarize data graphically and

statistically, either manually or via a computer package.

5. Students are able to justify and interpret statistical/analytical scenarios that best fit

usiness solution.

6. Students are able to justify value and limitations of the statistical techniques to business

decision making.

Description: Each week students were provided with three tutorial questions of varying degrees of

difficulty. These 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 7 to 11 inclusive and submit these answers in a single document.

The questions to be answered are;

Week 7

Question 2 (10 marks)

A local health centre noted that in a sample of 400 patients, 80 were refe

ed to them by the local

hospital.

a. Provide a 95% confidence interval for all the patients who are refe

ed to the health centre by

the hospital XXXXXXXXXXmarks)

. What sample size would be required to estimate the proportion of all hospital refe

als to the

health centre with a margin of e

or of 0.04 or less at 95% confidence? (5 marks)

Week 8

Question 1 (10 marks)

The average starting salary of students who graduated from colleges of Business in 2009 was $48,400.

A sample of 100 graduates of 2010 showed an average starting salary of $50,000. Assume the standard

deviation of the population is known to be $8000. We want to determine whether or not there has

een a significant increase in the starting salaries.

Step 1. Statement of the hypothesis XXXXXXXXXXmarks)

Step 2. Standardised test statistic formula XXXXXXXXXXmark)

Step 3. State the level of significance XXXXXXXXXXmark)

Step 4. Decision Rule (Draw a bell to show rejection zone XXXXXXXXXXmarks)

Step 5. Calculation of the statistic XXXXXXXXXXmarks)

Step 6. Conclusion XXXXXXXXXXmarks)

Week 9

Question 3 (10 marks)

The data in the table below presents the hourly quantity of production for three lines of production

processes over the first 4 days in XYZ Company. Answer the questions based on the Excel Output given

elow.

Day Process 1 Process 2 Process 3

XXXXXXXXXX

XXXXXXXXXX

XXXXXXXXXX

XXXXXXXXXX

ANOVA: Single Factor

SUMMARY

Groups Count Sum Average Variance

Process XXXXXXXXXX66667

Process XXXXXXXXXX3333

Process XXXXXXXXXX3333

ANOVA

Source of Variation SS df MS F P value

Between Groups 32 ? ? ?

Within Groups 88 ? ?

Total XXXXXXXXXX

a. State the null and alternative hypothesis for single factor ANOVA. (1 mark)

. State the decision rule (α = XXXXXXXXXXmarks)

c. Calculate the test statistic XXXXXXXXXXmarks)

d. Make a decision XXXXXXXXXXmarks)

Week 10

Question 2 (10 marks)

Personal wealth tends to increase with age as older individuals have had more opportunities

to earn and invest than younger individuals. The following data were obtained from a random

sample of eight individuals and records their total wealth (Y) and their cu

ent age (X).

Person Total wealth (‘000s of dollars)

Y

Age (Years)

X

A 280 36

B 450 72

C 250 48

D 320 51

E 470 80

F 250 40

G 330 55

H 430 72

A part of the output of a regression analysis of Y against X using Excel is given below:

SUMMARY OUTPUT

Regression Statistics

Multiple R XXXXXXXXXX

R Square XXXXXXXXXX

Adjusted R Square XXXXXXXXXX

Standard E

or XXXXXXXXXX

Observations 8

ANOVA

df SS MS F Significance F

Regression XXXXXXXXXX

Residual XXXXXXXXXX

Total XXXXXXXXXX

Coefficients Standard E

or t Stat P-value

Intercept XXXXXXXXXX

Age XXXXXXXXXX

a. State the estimated regression line and interpret the slope coefficient. (1.5 marks)

. What is the estimated total personal wealth when a person is 50 years old? (1

mark)

c. What is the value of the coefficient of determination? Interpret it XXXXXXXXXXmarks)

d. Test whether there is a significant relationship between wealth and age at the 10%

significance level. Perform the test using the following six steps.

Step 1. Statement of the hypotheses XXXXXXXXXXmark)

Step 2. Standardised test statistic XXXXXXXXXXmark)

Step 3. Level of significance XXXXXXXXXXmark)

Step 4. Decision Rule XXXXXXXXXXmarks)

Step 5. Calculation of test statistic XXXXXXXXXXmarks)

Step 6. Conclusion XXXXXXXXXXmark)

Week 11

Question 3 (10 marks)

A student used multiple regression analysis to study how family spending (y) is influenced by income

(x1), family size (x2), and additions to savings (x3). The variables y, x1, and x3 are measured in thousands

of dollars. The following results were obtained.

ANOVA

df SS

Regression XXXXXXXXXX

Residual XXXXXXXXXX

Total

Coefficients Standard E

or

Intercept XXXXXXXXXX

x XXXXXXXXXX

x XXXXXXXXXX

x XXXXXXXXXX

a. Write out the estimated regression equation for the relationship between the variables. (1

mark)

. Compute coefficient of determination. What can you say about the strength of this

elationship? XXXXXXXXXXmarks)

c. Ca

y out a test to determine whether y is significantly related to the independent variables.

Use a 5% level of significance XXXXXXXXXXmarks)

d. Ca

y out a test to see if x3 and y are significantly related. Use a 5% level of significance. (3

marks)

Submission Directions:

The assignment has to be submitted via Blackboard. Each student will be permitted one

submission to Blackboard only. Each student needs to ensure that the document submitted

is the co

ect one.

Academic Integrity

Academic honesty is highly valued at Holmes Institute. Students must always submit work

that represents their original words or ideas. If any words or ideas used in a class posting or

assignment submission do not represent the student’s original words or ideas, the student

must cite all relevant sources and make clear the extent to which such sources were used.

Written assignments that include material similar to course reading materials or other

sources should include a citation including source, author, and page number.

In addition, written assignments that are similar or identical to those of another student in

the class 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 to suspension of enrolment. The penalty would be dependent on the

extent of academic misconduct and the student’s 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, students should refer to their Discussion

Board for the unit.

Unit Code: HI6007

Unit Name: Statistics for Business Decisions

Assignment: Tutorial Questions 2

Due: 11:59PM 19 June 2020

Weighting: 25%

Purpose: This assignment is designed to assess your level of knowledge of the key topics covered in

this unit

Unit Learning Outcomes Assessed:

1. Students are able to apply appropriate business research methodologies to support

decision-making process.

2. Students are able to identify and apply valid statistical techniques in a given scenario to

solve business problems.

3. Students are able to justify and interpret the results of a statistical analysis in the context

of critical reasoning for a business problem solving.

4. Students are able to apply statistical knowledge to summarize data graphically and

statistically, either manually or via a computer package.

5. Students are able to justify and interpret statistical/analytical scenarios that best fit

usiness solution.

6. Students are able to justify value and limitations of the statistical techniques to business

decision making.

Description: Each week students were provided with three tutorial questions of varying degrees of

difficulty. These 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 7 to 11 inclusive and submit these answers in a single document.

The questions to be answered are;

Week 7

Question 2 (10 marks)

A local health centre noted that in a sample of 400 patients, 80 were refe

ed to them by the local

hospital.

a. Provide a 95% confidence interval for all the patients who are refe

ed to the health centre by

the hospital XXXXXXXXXXmarks)

. What sample size would be required to estimate the proportion of all hospital refe

als to the

health centre with a margin of e

or of 0.04 or less at 95% confidence? (5 marks)

Week 8

Question 1 (10 marks)

The average starting salary of students who graduated from colleges of Business in 2009 was $48,400.

A sample of 100 graduates of 2010 showed an average starting salary of $50,000. Assume the standard

deviation of the population is known to be $8000. We want to determine whether or not there has

een a significant increase in the starting salaries.

Step 1. Statement of the hypothesis XXXXXXXXXXmarks)

Step 2. Standardised test statistic formula XXXXXXXXXXmark)

Step 3. State the level of significance XXXXXXXXXXmark)

Step 4. Decision Rule (Draw a bell to show rejection zone XXXXXXXXXXmarks)

Step 5. Calculation of the statistic XXXXXXXXXXmarks)

Step 6. Conclusion XXXXXXXXXXmarks)

Week 9

Question 3 (10 marks)

The data in the table below presents the hourly quantity of production for three lines of production

processes over the first 4 days in XYZ Company. Answer the questions based on the Excel Output given

elow.

Day Process 1 Process 2 Process 3

XXXXXXXXXX

XXXXXXXXXX

XXXXXXXXXX

XXXXXXXXXX

ANOVA: Single Factor

SUMMARY

Groups Count Sum Average Variance

Process XXXXXXXXXX66667

Process XXXXXXXXXX3333

Process XXXXXXXXXX3333

ANOVA

Source of Variation SS df MS F P value

Between Groups 32 ? ? ?

Within Groups 88 ? ?

Total XXXXXXXXXX

a. State the null and alternative hypothesis for single factor ANOVA. (1 mark)

. State the decision rule (α = XXXXXXXXXXmarks)

c. Calculate the test statistic XXXXXXXXXXmarks)

d. Make a decision XXXXXXXXXXmarks)

Week 10

Question 2 (10 marks)

Personal wealth tends to increase with age as older individuals have had more opportunities

to earn and invest than younger individuals. The following data were obtained from a random

sample of eight individuals and records their total wealth (Y) and their cu

ent age (X).

Person Total wealth (‘000s of dollars)

Y

Age (Years)

X

A 280 36

B 450 72

C 250 48

D 320 51

E 470 80

F 250 40

G 330 55

H 430 72

A part of the output of a regression analysis of Y against X using Excel is given below:

SUMMARY OUTPUT

Regression Statistics

Multiple R XXXXXXXXXX

R Square XXXXXXXXXX

Adjusted R Square XXXXXXXXXX

Standard E

or XXXXXXXXXX

Observations 8

ANOVA

df SS MS F Significance F

Regression XXXXXXXXXX

Residual XXXXXXXXXX

Total XXXXXXXXXX

Coefficients Standard E

or t Stat P-value

Intercept XXXXXXXXXX

Age XXXXXXXXXX

a. State the estimated regression line and interpret the slope coefficient. (1.5 marks)

. What is the estimated total personal wealth when a person is 50 years old? (1

mark)

c. What is the value of the coefficient of determination? Interpret it XXXXXXXXXXmarks)

d. Test whether there is a significant relationship between wealth and age at the 10%

significance level. Perform the test using the following six steps.

Step 1. Statement of the hypotheses XXXXXXXXXXmark)

Step 2. Standardised test statistic XXXXXXXXXXmark)

Step 3. Level of significance XXXXXXXXXXmark)

Step 4. Decision Rule XXXXXXXXXXmarks)

Step 5. Calculation of test statistic XXXXXXXXXXmarks)

Step 6. Conclusion XXXXXXXXXXmark)

Week 11

Question 3 (10 marks)

A student used multiple regression analysis to study how family spending (y) is influenced by income

(x1), family size (x2), and additions to savings (x3). The variables y, x1, and x3 are measured in thousands

of dollars. The following results were obtained.

ANOVA

df SS

Regression XXXXXXXXXX

Residual XXXXXXXXXX

Total

Coefficients Standard E

or

Intercept XXXXXXXXXX

x XXXXXXXXXX

x XXXXXXXXXX

x XXXXXXXXXX

a. Write out the estimated regression equation for the relationship between the variables. (1

mark)

. Compute coefficient of determination. What can you say about the strength of this

elationship? XXXXXXXXXXmarks)

c. Ca

y out a test to determine whether y is significantly related to the independent variables.

Use a 5% level of significance XXXXXXXXXXmarks)

d. Ca

y out a test to see if x3 and y are significantly related. Use a 5% level of significance. (3

marks)

Submission Directions:

The assignment has to be submitted via Blackboard. Each student will be permitted one

submission to Blackboard only. Each student needs to ensure that the document submitted

is the co

ect one.

Academic Integrity

Academic honesty is highly valued at Holmes Institute. Students must always submit work

that represents their original words or ideas. If any words or ideas used in a class posting or

assignment submission do not represent the student’s original words or ideas, the student

must cite all relevant sources and make clear the extent to which such sources were used.

Written assignments that include material similar to course reading materials or other

sources should include a citation including source, author, and page number.

In addition, written assignments that are similar or identical to those of another student in

the class 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 to suspension of enrolment. The penalty would be dependent on the

extent of academic misconduct and the student’s 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, students should refer to their Discussion

Board for the unit.

Week 7: Question 2:

The number patient in the health centre is:

Out of 400 patients, the number of patients refe

ed to them by the local hospital is:

Calculate the sample proportion value.

a)

Calculate the 95% confidence interval for all the patients who are refe

ed to the health centre by the hospital.

From the standard normal tables, the critical value at the 95% confidence level is 1.960.

Hence, the required confidence interval is:

)

Calculate the sample size would be required to estimate the proportion of all hospital refe

als to the health centre.

Here, the Margin of e

or is:

Hence, the required sample size is: 385.

Week 8: Question-1:

The average starting salary of student who graduated from college of Business is:

The number of graduates of 2010 is:

The sample average is:

The population standard deviation is:

Note: the population standard deviation in known, so we use standard normal test

Step-1:

Null hypothesis,

Alternative hypothesis,

Step-2:

The formula for the standardized test statistic is:

Step-3:

The level of significance is:

From the standard normal tables, the critical value at the 0.05 level of significance is: 1.645 (Right tailed test)

Step-4:

Decision rule: Reject if

The graphical representation is shown in below,

Step-5:

Calculate the test statistic value.

Step-6:

Decision: Reject because, the test statistic value (2.00) is greater than the 1.645.

Conclusion: there is enough evidence to conclude that there has been a significant increase in the starting salaries.

Week-9: Question-3:

Calculate the missing values in the ANOVA table.

The number of groups: (Process-1, Process-2, Process-3)

The number of observations in the given table is:

a)

Null hypothesis,

Alternative hypothesis, At least one mean is different from others.

)

Decision rule: Reject if value is less than the 0.05 level of significance.

c)

Calculate the test statistic value.

d)

Decision: Fail to reject because, the value (0.2477) is greater than the 0.05 level of significance.

Conclusion: there is not enough evidence to conclude that the 3 companies means is differ at the 0.05 level of significance.

Week-10: Question-2:

a)

From the given information:

The slope coefficient is:

The intercept coefficient is:

The estimated regression equation is shown in below,

Slope interpretation: the slope coefficient is...

The number patient in the health centre is:

Out of 400 patients, the number of patients refe

ed to them by the local hospital is:

Calculate the sample proportion value.

a)

Calculate the 95% confidence interval for all the patients who are refe

ed to the health centre by the hospital.

From the standard normal tables, the critical value at the 95% confidence level is 1.960.

Hence, the required confidence interval is:

)

Calculate the sample size would be required to estimate the proportion of all hospital refe

als to the health centre.

Here, the Margin of e

or is:

Hence, the required sample size is: 385.

Week 8: Question-1:

The average starting salary of student who graduated from college of Business is:

The number of graduates of 2010 is:

The sample average is:

The population standard deviation is:

Note: the population standard deviation in known, so we use standard normal test

Step-1:

Null hypothesis,

Alternative hypothesis,

Step-2:

The formula for the standardized test statistic is:

Step-3:

The level of significance is:

From the standard normal tables, the critical value at the 0.05 level of significance is: 1.645 (Right tailed test)

Step-4:

Decision rule: Reject if

The graphical representation is shown in below,

Step-5:

Calculate the test statistic value.

Step-6:

Decision: Reject because, the test statistic value (2.00) is greater than the 1.645.

Conclusion: there is enough evidence to conclude that there has been a significant increase in the starting salaries.

Week-9: Question-3:

Calculate the missing values in the ANOVA table.

The number of groups: (Process-1, Process-2, Process-3)

The number of observations in the given table is:

a)

Null hypothesis,

Alternative hypothesis, At least one mean is different from others.

)

Decision rule: Reject if value is less than the 0.05 level of significance.

c)

Calculate the test statistic value.

d)

Decision: Fail to reject because, the value (0.2477) is greater than the 0.05 level of significance.

Conclusion: there is not enough evidence to conclude that the 3 companies means is differ at the 0.05 level of significance.

Week-10: Question-2:

a)

From the given information:

The slope coefficient is:

The intercept coefficient is:

The estimated regression equation is shown in below,

Slope interpretation: the slope coefficient is...

SOLUTION.PDF## Answer To This Question Is Available To Download

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