BCO 127 MU Applied Management Statistics Hypothesis Tests Questions

BCO127
Applied Management Statistics
Task brief & rubrics
Task
The following points relate to the Final Assignment in Week 8:
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This is an individual task and no group work is allowed
All questions in the Final Assignment are to be answered
All calculations and interpretations are to be provided in Word (or PDF or Excel) format.
Task Briefing
The below table shows the sales per year given the expenditure on advertising and the number of employees for the respective year.
Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Sales (millions
Euros)
651
762
856
1063
1190
1298
1421
1440
1518
1590
1650
1800
1820
1900
1950
2050
2100
2180
2260
2320
Advertising (thousands
Euros)
23
26
30
34
43
48
52
57
58
58
62
70
65
68
72
72
73
74
76
78
Number of
Employees
10
12
16
20
22
22
23
25
25
25
27
37
38
38
40
40
41
42
43
44
1.) Do you think that the amount spent on advertising every year made an impact on the annual sales? (25 points)
Discuss your answer by making use of a Hypothesis Test and given that the sales prior to investing in advertising for the previous 20 years were as follows:
Sales
Before
455.7 533.4 599.2 744.1
Advertising
833
908.6 994.7 1008 1062.6 1113 1155 1260 1274 1330 1365 1435 1470 1526 1582 1624
(TIP: If there was an improvement in sales then the average of sales would have increased)
1.1 What do you think is the most appropriate Hypothesis Test?
1.2 What is the Null Hypothesis? What is the Alternative Hypothesis?
1.3 By making use of a t-test, assess whether or not advertising has led to a significant increase in sales. Present your results as well as interpret the
results.
2.) Assume the variable annual sales follows a Normal Distribution. Estimate the population mean with a Confidence Interval of 95%. (20 points).
3.) Use the above table of data and choose a Simple Random Sample (SRS) of five. Start at the beginning of the list and attach labels to the years. What sample
do you obtain? Show all your steps. (10 points)
4.) Determine the relationship between advertising and sales. (35 points)
a. Plot a Scatter plot of the data (sales vs advertising). Interpret the plot?
b. Calculate the linear regression equation that best fits the data and explains the independent and dependent variables. (TIP: dependent variable =
Sales; independent variables = Advertising & Number of Employees).
c. Calculate the correlation coefficient and interpret the result.
d. Estimate the sales for the 21st year of business if advertising is 90 and the number of employees as 50.
e. Estimate the sales for the 22nd year of business if advertising is 100 and the number of employees as 55.
f. Interpret the Goodness of Fit measure for the regression model provided in (a.).
Formalities:
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Wordcount: 1000 – 1500
Cover, Table of Contents, References and Appendix are excluded of the total wordcount.
Font: Arial 12,5 pts.
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Text alignment: Justified.
The in-text References and the Bibliography have to be in Harvard’s citation style.
Submission: Week 8 – Via Moodle (Turnitin). 20 September 2020, 23:59.
Weight: This task is a 60% of your total grade for this subject.
It assesses the following learning outcomes:
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Understand the complex calculations, methodologies and techniques to derive a sound conclusion
Understand statistical language and the development of statistical thinking
Ability to understand and answer complex statistical problems
Ability to interpret calculated results and provide insight to the questions asked
Rubrics
Application (30%)
Student applies fully
relevant knowledge from
the topics delivered in
class.
Good 80-89
Student demonstrates
good understanding of the
task and mentions some
relevant concepts and
demonstrates use of the
relevant vocabulary.
Student applies mostly
relevant knowledge from
the topics delivered in
class.
Critical Thinking
(30%)
Student critically assesses
in excellent ways, drawing
outstanding conclusions
from relevant authors.
Student critically assesses
in good ways, drawing
conclusions from relevant
authors and references.
Communication
(20%)
Student communicates
their ideas extremely
clearly and concisely,
respecting word count,
grammar and spellcheck
Student communicates
their ideas clearly and
concisely, respecting word
count, grammar and
spellcheck
Knowledge &
Understanding
(20%)
Exceptional 90-100
Student demonstrates
excellent understanding of
key concepts and uses
vocabulary in an entirely
appropriate manner.
Fair 70-79
Student understands the
task and provides minimum
theory and/or some use of
vocabulary.
Student applies some
relevant knowledge from
the topics delivered in
class. Misunderstanding
may be evident.
Student provides some
insights but stays on the
surface of the topic.
References may not be
relevant.
Student communicates
their ideas with some
clarity and concision. It
may be slightly over or
under the wordcount limit.
Some misspelling errors
may be evident.
Marginal fail 60-69
Student understands the task
and attempts to answer the
question but does not
mention key concepts or uses
minimum amount of relevant
vocabulary.
Student applies little relevant
knowledge from the topics
delivered in class.
Misunderstands are evident.
Student makes little or none
critical thinking insights, does
not quote appropriate
authors, and does not
provide valid sources.
Student communicates their
ideas in a somewhat unclear
and unconcise way. Does not
reach or does exceed
wordcount excessively and
misspelling errors are
evident.