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Assessment Task–Tutorial QuestionsUnit Code: HI6007

Unit Name: Statistics for Business Decisions Assignment: Tutorial Questions 2

Due: 11:59PM 19 June 2020Weighting: 25%

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

Unit Learning Outcomes Assessed:

Students are able to apply appropriate business research methodologies to support decision-making process.

Students are able to identify and apply valid statistical techniques in a given scenario to solve business problems.

Students are able to justify and interpret the results of a statistical analysis in the context of critical reasoning for a business problem solving.

Students are able to apply statistical knowledge to summarize data graphically and statistically, either manually or via a computer package.

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

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

Question2(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

Question1(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

Step 2. Standardised test statistic formula

Step 3. State the level of significance

Step 4. Decision Rule (Draw a bell to show rejection zone) Step 5. Calculation of the statistic

Step 6. Conclusion

Week 9

Question3(10 marks)

(1.5 marks) (1 mark)

(1 mark)

(3 marks) (2 marks) (1.5 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

Process 1 Process 2 Process 3

ANOVA

Source of Variation

Between Groups Within Groups

Total

Count

4 4 4

SS

32 88

120

Sum

XXXXXXXXXX

Average

XXXXXXXXXX

Variance

XXXXXXXXXX3333

df

? ?

11

MS

? ?

F

?

P value

(1 mark) (4 marks) (3 marks) (2 marks)

State the null and alternative hypothesis for single factor ANOVA.

State the decision rule (α= 0.05).

Calculate the test statistic.

Make a decision.

Week 10

Question2(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

R Square

Adjusted R Square Standard Error Observations

ANOVA

XXXXXXXXXX XXXXXXXXXX

df

SS

XXXXXXXXXX56950

Standard Error

XXXXXXXXXX

MS F

XXXXXXXXXX

t Stat P-value

Significance F

Regression 1 Residual 6 Total 7

Coefficients

Intercept XXXXXXXXXXAge 5.3265

State the estimated regression line and interpret the slope coefficient.

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

mark)

What is the value of the coefficient of determination? Interpret it. (1.5 marks)

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)

(1.5 marks)

Step 5. Calculation of test statistic (1.5 marks) Step 6. Conclusion (1 mark)

Week 11

Question3(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 variablesy,x1, andx3are 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 |

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 relationship? (3 marks)

Carry out a test to determine whether y is significantly related to the independent variables. Use a 5% level of significance. (3 marks)

Carry out a test to see if x3and 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 representthe student’soriginal 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 IntegrityPolicy. 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.

a. Confidence interval

No of patients = n = 400

Selected patients = 80

p = 80/400 = 0.2

q = 1-P = 0.8

95% confidence Interval = p ± 1.96

95% confid

95% confidence Interval:

Upper limit = 8.2

Lower Limit = -7.8

. Sample Size Required

E

or = 0.04

Prob [ |P’ – P| 1.96 ] = 0.95

This implies:

1.96 = 0.95

Solving for n

n = 384

Sample Size = 384

WEEK 8

2009

2010

Average Salary

$ 48,400

$ 50,000

Standard Deviation of Population =

$ 8,000

Size of Sample = 100

Hypothesis

Null Hypothesis: There is no significant increase in average salaries i.e.

Alternative Hypothesis: There is significant increase in average salaries i.e. Average Salary of 2010 is greater than Average Salary of 2009 i.e.

Standardize the Test Statistic

Standardized test statistic =

Level of significance

Level of significance = 1- Confidence level

Level of significance = 1 -0.95 = 0.05

Decision Rule = Z value = 1.96

Test Statistics

t = = 1.41

Conclusion

Since t statistic is 1.41 which is less than 1.96, therefore, we fail to reject null hypothesis and may conclude that there is no significant difference in the average salaries of 2009 and 2010.

WEEK 9

Day 1

Process 1

Process 2

Process 3

1

33

33

28

2

30

35

36

3

28

30

30

4

29

38

34

Anova: Single Facto

SUMMARY

Groups

Count

Sum

Average

Variance

Process 1

4

120

30

4.66666667

Process 2

4

136

34

11.3333333

Process...

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

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