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 business 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 referred to them by the local hospital.

a. Provide a 95% confidence interval for all the patients who are referred to the health centre by the hospital. (5 marks)

b. What sample size would be required to estimate the proportion of all hospital referrals to the health centre with a margin of error 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 been a significant increase in the starting salaries.

Step 1. Statement of the hypothesis (1.5 marks)

Step 2. Standardised test statistic formula (1 mark)

Step 3. State the level of significance (1 mark)

Step 4. Decision Rule (Draw a bell to show rejection zone) (3 marks)

Step 5. Calculation of the statistic (2 marks)

Step 6. Conclusion (1.5 marks)

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 below.

Day Process 1 Process 2 Process 3

1 33 33 28

2 30 35 36

3 28 30 30

4 29 38 34

ANOVA: Single Factor

SUMMARY

Groups Count Sum Average Variance

Process 1 4 120 30 4.66667

Process 2 4 136 34 11.3333

Process 3 4 128 32 13.3333

ANOVA

Source of Variation SS df MS F P value

Between Groups 32 ? ? ?

Within Groups 88 ? ?

Total 120 11

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

b. State the decision rule (a = 0.05). (4 marks)

c. Calculate the test statistic. (3 marks)

d. Make a decision. (2 marks)

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 current 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 0.954704

R Square 0.91146

Adjusted R Square 0.896703

Standard Error 28.98954

Observations 8

ANOVA

df SS MS F Significance F

Regression 1 51907.64 51907.64

Residual 6 5042.361 840.3936

Total 7 56950

Coefficients Standard Error t Stat P-value

Intercept 45.2159 39.8049

Age 5.3265 0.6777

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

b. 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. (1.5 marks)

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 (1 mark)

Step 2. Standardised test statistic (0.5 mark)

Step 3. Level of significance (0.5 mark)

Step 4. Decision Rule (1.5 marks)

Step 5. Calculation of test statistic (1.5 marks)

Step 6. Conclusion (1 mark)

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 3 45.9634

Residual 11 2.6218

Total

Coefficients Standard Error

Intercept 0.0136

x1 0.7992 0.074

x2 0.2280 0.190

x3 -0.5796 0.920

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

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

relationship? (3 marks)

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

Use a 5% level of significance. (3 marks)

d. Carry 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 correct 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 business 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 referred to them by the local hospital.

a. Provide a 95% confidence interval for all the patients who are referred to the health centre by the hospital. (5 marks)

b. What sample size would be required to estimate the proportion of all hospital referrals to the health centre with a margin of error 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 been a significant increase in the starting salaries.

Step 1. Statement of the hypothesis (1.5 marks)

Step 2. Standardised test statistic formula (1 mark)

Step 3. State the level of significance (1 mark)

Step 4. Decision Rule (Draw a bell to show rejection zone) (3 marks)

Step 5. Calculation of the statistic (2 marks)

Step 6. Conclusion (1.5 marks)

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 below.

Day Process 1 Process 2 Process 3

1 33 33 28

2 30 35 36

3 28 30 30

4 29 38 34

ANOVA: Single Factor

SUMMARY

Groups Count Sum Average Variance

Process 1 4 120 30 4.66667

Process 2 4 136 34 11.3333

Process 3 4 128 32 13.3333

ANOVA

Source of Variation SS df MS F P value

Between Groups 32 ? ? ?

Within Groups 88 ? ?

Total 120 11

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

b. State the decision rule (a = 0.05). (4 marks)

c. Calculate the test statistic. (3 marks)

d. Make a decision. (2 marks)

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 current 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 0.954704

R Square 0.91146

Adjusted R Square 0.896703

Standard Error 28.98954

Observations 8

ANOVA

df SS MS F Significance F

Regression 1 51907.64 51907.64

Residual 6 5042.361 840.3936

Total 7 56950

Coefficients Standard Error t Stat P-value

Intercept 45.2159 39.8049

Age 5.3265 0.6777

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

b. 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. (1.5 marks)

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 (1 mark)

Step 2. Standardised test statistic (0.5 mark)

Step 3. Level of significance (0.5 mark)

Step 4. Decision Rule (1.5 marks)

Step 5. Calculation of test statistic (1.5 marks)

Step 6. Conclusion (1 mark)

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 3 45.9634

Residual 11 2.6218

Total

Coefficients Standard Error

Intercept 0.0136

x1 0.7992 0.074

x2 0.2280 0.190

x3 -0.5796 0.920

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

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

relationship? (3 marks)

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

Use a 5% level of significance. (3 marks)

d. Carry 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 correct 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.

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