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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...

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
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
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
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 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.
Answered Same Day Jun 12, 2021 HI6007

## Solution

Aarti answered on Jun 15 2021
Week 7
Question 2)
Solution (a):
Given,
Sample size (n) = 400
Probability of success (p) = 80/400 = 0.2
The 95% confidence interval is calculated as:

The 95% confidence interval of the proportion lies with 0.1608 and 0.2392.
Solution (b):
Given,
Sample size (n) = 400
Probability of success (p) = 80/400 = 0.2
E
or (E) = 0.04
Level of significance () = 0.05
The sample size is calculated using the following :

The sample size is 385.
Week 8
Question 2)
Solution (a):
Given,
Population mean () = 48400
Sample size (n) = 100
Sample mean () = 50000
Population standard deviation () = 8000
Step 1:
The null and alternative hypothesis are as follows:

Step 2:
The standardized test formula is (also used to calculate the test statistics):

Step 3:
Let the significance level () = 0.05. As the population standard deviation is given, we use Z test. Here, it is a one tail test, the critical value is +1.96.
Step 4:
The decision rule is based on:
If the test statistics > critical value, we reject the null hypothesis.
If the test statistics < critical value, we do not reject the null hypothesis.
Decision rule based on the rejection region:
Step 5:
The test statistics is calculated using the above formula:

Step 6:
Conclusion:
Here, the test statistics is larger than the critical value, i.e. (1.96 < 2). We have to reject the null hypothesis. Therefore, we have enough evidence to show that the average starting salary of students is greater than 48400.
Week 9
Question 3)
Solution (a):
The null and alternative hypothesis are as follows:

Solution (b):
If the test statistics > critical value, we reject the null hypothesis.
If the test statistics < critical value, we do not reject the null...
SOLUTION.PDF