Assessment Task – Tutorial Questions
Unit Code: HI6007
Unit Name: Statistics for Business Decisions
Assignment: Tutorial Questions Assignment
Weighting: 50%
Purpose: This assignment is designed to assess your level of knowledge of the key topics covered in this unit
Unit Learning Outcomes Assessed.:
Description: Each week students were provided with three tutorial questions of varying degrees of difficulty. The 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 question for weeks 1 to 11 inclusive and submit these answers in a single document.
The questions to be answered are;
Question 1 (7 marks)
Question 2 (7 marks)
Annual food consumption survey shows that number of instant food meals consumed per month by university students is normally distributed with a mean of 10 and a standard deviation of 3.
Question 3 (11 marks)
D Dax limited installed a new safety equipment in order to reduce the number of person hours lost as a result of industrial accident. In a test to of the effectiveness of the equipment, a random sample of 50 departments was chosen. The number of person hours lost in the month prior to and the month after the installation of the safety equipment was recorded. The percentage change was calculated and recorded. Assume that the population standard deviation is 5 and sample mean is 1.2. Can we infer at the 10% significance level that the new safety equipment is effective?
You are required to
Question 4 (11 marks)
The table below shows data on research to examine the perception of business ethics among 3 groups of employees (higher score indicates higher ethical values).
A 
B 
C 
6 
5 
6 
5 
5 
7 
4 
4 
6 
5 
4 
5 
6 
5 
6 
4 
4 
6 
5 
5 
6 
4 
6 
6 
6 
5 
4 
5 
6 
5 
Note: No excel ANOVA output allowed. Students need to show all the steps in calculations.
Question 5 (7 marks)
Relax mortgage has gathered following data to examine the relationship between housing starts and mortgage interest rate.
Interest rate 
3.5 
3.0 
2.8 
3.6 
2.75 
3.4 
3.12 
2.86 
3.02 
2.6 
3.3 
Housing starts 
100 
120 
150 
130 
170 
135 
130 
185 
127 
190 
96 
You are required to;
Question 6 (7 marks)
D& T LTD marketing team needed more information about the effectiveness of their 3 main mode of advertising. To determine which type is the most effective, the manager collected one week’s data from 25 randomly selected stores. For each store, the following variables were recorded:
Weekly gross sales
Weekly expenditure on direct mailing (Direct)
Weekly expenditure on newspaper advertising (Newspaper)
Weekly expenditure on television commercials (Television)
Following is the regression output based on the abovementioned data.
SUMMARY OUTPUT 

Regression Statistics Multiple R 
0.442 
R Square 
A 
Adjusted R Square 
0.080 
Standard Error 
2.587 
Observations 
25 
ANOVA 
Df 
SS 
MS 
F 
Significance F 

Regression 
B 
34.1036 
E 
F 
0.1979 

Residual 
21 
D 
6.6933 

Total 
C 
174.6631 


Coefficients 
Standard Error 
t Stat 
Pvalue 
Lower 95% 
Intercept 12.31 4.70 2.62 0.02 
2.54 

Direct 0.57 1.72 H 0.74 
3.01 

Newspaper 3.32 1.54 2.16 0.04 
0.12 

Television G 1.96 0.37 0.71 
3.34 

a. Complete the missing entries from A to H in this output 
(2 marks) 

b. Assess the independent variables significance at 5% level 
(3 marks) 

c. Does the model is significant at 5% level? 
(2 marks) 
FORMULA SHEET
Location of the p^{th} percentile:
πΏπ= ^{π }(π+1)
100
IQR = Q_{3} – Q_{1 }
Expected value of a discrete random variable
πΈ
Variance of a discrete random variable
πππ
Z and t formulas:
π₯−π Μ π ππ₯Μ π π = π π π‘ _{ π }
πππ
π
Confidence intervals
Mean:
π
π₯Μ
Μ
πΜ
π§_{πΌ}^{2}_{/}2 π π
π = π΅_{2 }
Time Series Regression
π
π_{0 }= π − π_{1}π‘
π_{π‘ }= π_{0 }+ π_{1}π‘
ANOVA:
ππππ
MSTR
π _{2}
SSTR = ∑ π_{π}(π₯_{π}Μ − π₯ΜΏ)
π=1
π
SSE = ∑(π_{π }− 1)π _{π}^{2}
π=1
Simple Linear Regression:
Μπ¦ = π_{0 }+ π_{1}π₯
∑(π₯_{π }− π₯Μ )(π¦_{π }− π¦Μ )
π_{1 }= ∑(π₯_{π }− π₯Μ )_{2 } SSE
MSE =
π_{π }− π
π ππ
2 SST = ∑ ∑(π₯_{ππ }− π₯ΜΏ)
π=1 π=1
F = MSTR / MSE
π_{0 }= π¦Μ − π_{1}π₯Μ
SST = SSR + SSE
SSE = ∑(π¦_{π }− π¦Μ_{π})^{2} SST = ∑(π¦_{π }− π¦Μ )^{2}
SSR= ∑(π¦Μ_{π }− π¦Μ )^{2}
Coefficient of determination
R^{2}= SSR/SST
Correlation coefficient
π
π or π
R2 = (ππ₯π¦ )2
π_{π₯π¦ }= (sign of π_{1}) Coefficient of Determination
Testing for Significance
s = MSE = SSE/(n 2) s =
^{ }^{π }^{π} π Μ ^{π‘ = }π π_{π1}1^{ }F = MSTR / MSE
MSR = SSR/k1 MSE = SSE/nk
Confidence Interval for β_{1}
π1 ± π‘πΌ/2π π_{1}
Multiple Regression:
y = ο’ + ο’x + ο’x +. . . + ο’x + ο₯
0 1 1 2 2 p p
π¦Μ = b + b x + b x + . . . + b x
0 1 1 2 2 p p
^{2 2}) π
π _{π }= 1 − (1 − π
π
R^{2} = SSR/SST
\F distribution
Submission Directions:
The assignment will be submitted via Blackboard. Each student will be permitted only ONE submission to Blackboard. You need to ensure that the document submitted is the correct one.
Academic Integrity
Holmes Institute is committed to ensuring and upholding Academic Integrity, as Academic Integrity is integral to maintaining academic quality and the reputation of Holmes’ graduates. Accordingly, all assessment tasks need to comply with academic integrity guidelines. Table 1 identifies the six categories of Academic Integrity breaches. If you have any questions about Academic Integrity issues related to your assessment tasks, please consult your lecturer or tutor for relevant referencing guidelines and support resources. Many of these resources can also be found through the Study Skills link on Blackboard.
Academic Integrity breaches are a serious offence punishable by penalties that may range from deduction of marks, failure of the assessment task or unit involved, suspension of course enrolment, or cancellation of course enrolment.
Table 1: Six categories of Academic Integrity breaches
Plagiarism 
Reproducing the work of someone else without attribution. When a student submits their own work on multiple occasions this is known as selfplagiarism. 
Collusion 
Working with one or more other individuals to complete an assignment, in a way that is not authorised. 
Copying 
Reproducing and submitting the work of another student, with or without their knowledge. If a student fails to take reasonable precautions to prevent their own original work from being copied, this may also be considered an offence. 
Impersonation 
Falsely presenting oneself, or engaging someone else to present as oneself, in an inperson examination. 
Contract cheating 
Contracting a third party to complete an assessment task, generally in exchange for money or other manner of payment. 
Data fabrication and falsification 
Manipulating or inventing data with the intent of supporting false conclusions, including manipulating images. 
Source: INQAAHE, 2020
If any words or ideas used the assignment submission do not represent your original words or ideas, you must cite all relevant sources and make clear the extent to which such sources were used.
In addition, written assignments that are similar or identical to those of another student 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 suspension of enrolment. The penalty would be dependent on the extent of academic misconduct and your 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 please refer to your Discussion Board for the unit.
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