# 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.

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