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 (α = 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 Step 2. Standardised test statistic Step 3. Level of significance Step 4. Decision Rule | (1 mark) (0.5 mark) (0.5 mark) (1.5 marks) |

Step 5. Calculation of test statistic Step 6. Conclusion | (1.5 marks) (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.