Management Statistics

Management Statistics

by B3ln4iNmum

ACTIVITY BRIEF FOR ASSESSMENT 2
ACADEMIC YEAR 2021 – 2022 – SPRING

Course BCO127 – Management Statistics (2CH/3ECTS)
Instructor Louisa Carlse

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Participation in all assessment activities stated in this document is required. An overall course total of 70
points is required to pass the course. Due dates and times are always in Geneva time.

Assessment 2
Description Due date and
time		 Weight of
course total
Task 2.1: Quiz on Sampling Distributions
Assessment type: Quiz
Description: Multiple choice questions on the topic of Sampling
Distributions.
For further details of this assessment task, please consult the activity
description on the relevant week of the course site.		 28 Mar. 22
14:00		 5%
Task 2.2: Quiz on Tests of Significance
Assessment type: Quiz
Description: Multiple choice questions on the topic of Tests of
Significance.
For further details of this assessment task, please consult the activity
description on the relevant week of the course site.		 01 May. 22
14:00		 5%
Main task
Task 2.3: Final Assignment
Assessment type: Written assignment
Description: Assignment on Sampling Distributions, Confidence
Intervals, Tests of Significance and Regression. Questions are
mostly practical – students will submit a spreadsheet file.
See sections below for further details.		 09 May. 22
14:00		 30%

INSTRUCTIONS
Main task
• Graphs should be titled, and all axes should be adequately labeled
• The submitted spreadsheet must include all formulas used and all necessary calculations to prove
steps taken for final answers
FORMAT
Your submission must meet the following formatting requirements:
• Submit one file only.
• Required file format for main submission: Excel spreadsheet (.xlsx).
• Additional file format for additional deliverables: Not applicable.
• Additional file requirements: None.
Other details:
• No specific formatting specifications
• No specific number of words required
• No referencing required
LEARNING OUTCOMES
• Understand concepts, formulas and techniques of statistics through exercises and applied examples;
• Understand statistical language, statistical context, uncertainty, and develop statistical thinking;
• Design statistical models, perform analysis, and solve real-world problems;
• Interpret results of statistical analysis
ASSESSMENT CRITERIA

Criteria Accomplished
(A)		 Proficient (B) Partially
proficient (C)		 Borderline (D) Fail (F)
Computation Result and
process are
correct, and
answer is well
explained
(process is
detailed). Minor
details may cause
deduction of
points.		 Minor errors
leading to wrong
result, but
computation is
clear and process
is generally
correct.		 Some important
errors revealing
some confusion,
but partially
correct process.
Seemingly
correct process
and correct
result, but no
adequate
explanation is
provided		 Important errors
revealing significant
misunderstanding
of relevant
concepts, but the
process is not
entirely wrong.		 Wrong result,
lacking any
coherent
explanation.
Written
Answers &
Interpretations		 Well detailed
and justified
answered,
statistically
correct.		 Well detailed
and justified
answered, with
some statistical
incorrections.		 Revels
understanding
of some
concepts, but
there is some
confusion
regarding
relevant topics.		 Incorrect answer
from the
statistical point of
view, but
explanation is not
completely
incoherent or
wrong		 Wrong
answer and
incoherent or
absent
justification.
Graph Correct, readable
and well
presented,
properly titled and
labeled (including
axes, and units if
needed)		 Some minor
readability or
presentation.		 Important errors,
but graphs still
conveys most
relevant
information.		 Serious errors
rendering the graph
almost useless, but
correct type of
graph and variables
are used.		 No graphs is
presented, or
graph
completely
misses the
point
(incorrect
graph type
and/or
variables)

ADDITIONAL INFORMATION
Question 1 (15 Marks)
Answer the following questions:

a) What is the difference between statistic and parameter? (5 points)
b) The variable Y follows a continuous uniform distribution. What is the type of distribution followed by the
sampling distribution of the mean of Y, for a sample size of 80? Justify. (5 points)
c) What is the meaning of “sampling distribution of the mean“ of a certain variable X, for a given sample
size n? (5 points)

Question 2 (25 Marks)

A certain successful restaurant operates with a waiting line, without reservations. The managers
want to know how much time in minutes (variable X) are the customers waiting and decide to run
a simple study. Before this study, the distribution of X was completely unknown. During a specific
day, a total of 80 customers were asked to measure the waiting time. Initially, a sample of 40
measurements (lunch) was obtained:
23.9 21.5 27.0 0.0 30.9 9.3 22.2 29.3
5.8 0.0 20.9 17.5 25.1 29.1 27.1 6.2
15.8 21.9 25.0 13.9 21.7 16.7 13.9 19.6
23.0 8.0 11.1 18.0 28.6 18.6 9.1 34.3
1.1 21.0 10.3 23.2 7.1 5.2 36.4 18.4
a) Based on this sample, compute a confidence interval for the mean of X, for a confidence level
of 95%. (10 points)
b) A new batch of 40 measurements arrives in the evening (dinner), allowing for a sample size
increase (n = 80). Compute a new interval estimate for the mean, for the same confidence level
of 95%, taking both the lunch and the dinner measurements into account (n = 80). (5 points)
32.9 35.5 33.7 43.4 39.0 29.0 38.0 32.7
35.3 22.0 38.4 31.5 25.5 39.4 41.7 22.1
36.3 42.3 33.7 29.4 0.0 36.5 32.5 29.2
30.6 34.7 11.2 34.5 8.7 23.2 36.7 19.2
33.4 44.0 39.2 33.7 15.7 26.5 0.0 46.5
c) Compare your answers to 2.1 and 2.2 and justify the difference(s). In your opinion, should the
managers attempt to obtain separate interval estimates for lunch and dinner? Justify. (5 points)
d) Assuming the standard deviation of the population is equal to the sample standard deviation
(sample of 80 measurements), determine the sample size required for a confidence interval with
a margin of error of 3 minutes and a confidence level of 95%. (5 points)

Question 3 (30 Marks)

A company that produces wireless headphones is testing a new battery for their products. In order to
evaluate the capacity of the new batteries, a sample of 50 headphones from a specific model are equipped
with the new battery and tested for autonomy. The current average battery autonomy is 5.2 hours. Test
results from the sample of headphones equipped with the new battery produce a sample mean of 5.6 hours
and a sample standard deviation of 0.8 hours. For a significance level of 5%, can we conclude that the
autonomy of the new batteries is different from the autonomy of the batteries currently in use?

 

a) Should this test for the mean be two-tailed, right-tailed or left-tailed? Justify your answer. (5 points)
b) State the null hypothesis (5 points)
c) State the alternative hypothesis. (5 points)
d) Compute the p-value and comment on the result. (5 points)
e) Compute the rejection region (test statistic) and use it to determine whether the null hypothesis should be
rejected, for a significance level of 5%. Do not forget to write a conclusion that refers to the real-world
problem, i.e. a conclusion that people without a background in Statistics may understand. (5 points)
f) Could you have answered the previous question (determining the test result for a significance level of 5%)
without computing the rejection region? Justify your answer. (5 points)

Question 4 (30 Marks)

A company that manufactures solar energy systems performs a study on the relationship between
average power obtained from a specific solar panel (X1, in kilowatt [kW]) and average daily rainfall (X2, in
mm). A sample of 30 solar panels is placed in different geographical locations and, after a few weeks, the
average power obtained by each solar panel is registered. Parallel measures of average daily rainfall for
those exact same locations are obtained:

 

X1. Average
power [kW]		 X2. Average
daily rainfall
[mm]
1.65 0.69
1.19 17.47
0.85 24.43
0.89 27.13
1.15 25.77
1.43 7.53
1.74 6.74
1.52 1.54
1.51 14.50
1.39 6.34
1.84 2.58
1.33 17.07
0.65 31.97
1.13 13.68
1.58 11.92
1.62 7.50
0.92 31.33
1.81 1.37
1.80 6.32
1.65 2.58
1.69 1.89
1.06 27.57
1.56 0.87
1.41 11.74
1.92 1.56
1.36 5.88
1.29 14.73
1.27 13.58
1.50 3.33
1.60 3.50
a) Compute the correlation between the two variables. (5 points)
b) In your opinion, which of the two variables (X1 and X2) should be considered as the independent or
explanatory variable in this case? Justify your answer. (5 points)
c) Based on your answer to the previous question, determine the coefficients of the linear regression
model. Write down the complete linear regression model. (5 points)
d) Compute the coefficient of determination (r² or R squared) of this model. What would the value of the
coefficient of determination be if the variables in the regression model were inverted – (independent or
explanatory variable (X) becomes Y, and dependent or response variable (Y) becomes X)? Justify. (5
points)
e) Predict the value of X2 for a solar panel that produces an average of 0.8 kW, using the linear model
you’ve determined in (c).
Predict the value of X1 for a panel installed in a location with an average daily rainfall of 20 mm, using the
linear model you’ve determine in (c). (5 points)
f) Obtain an appropriate graphical representation of the linear regression model. (note: in addition to the
original graph, please include or paste the graph as a picture to avoid any formatting or conversion issue).
(5 points).

 

QUALITY: 100% ORIGINAL PAPER – NO PLAGIARISM – CUSTOM PAPER

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