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#### HI6007 Statistics for Business Decisions

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## HI6007 Statistics for Business Decisions

Unit Code: HI6007

Unit Name: Statistics for Business Decisions

Due: 11:59PM 19 June 2020

Weighting: 25%

Purpose: HI6007 Statistics for Business Decisions 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 7Question 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 8Question 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 9Question 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 10Question 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 11Question 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 enrollment. 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 Self Assign to assess their originality.

Further Information:
For further information and additional learning resources, students should refer to their Discussion
Board for the unit.