Summary

Resit Assignment
This assignment is composed by 4 questions (with multiple subquestions), each in a separate sheet.
Instructions:
. You must submit a spreadsheet file with your answers (xlsx, ods). You can edit this file with your answers and submit it if you wish, or use a separate file.
. Graphs should be titled and the axes should be adequately labeled.
. Your file must be readable, and all answers must be identified by the question number.
. All the built-in functions (ex: AVERAGE()) must be included and visible – do not paste values computed elsewhere.
. A written explanation must be given when asked (ex: “Justify”).
Due date:
October 1, 2021, at 23:59 CET
Please read the resit brief for a detailed description, including the learning outcomes and grading rubrics.

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Q1

Question 1
The following table shows the distribution of the employees of a given company by department:
Department Frequency Relative Frequency
Accounting 9 0.0588
Legal 12 0.0784
Maintenance 14 0.0915
Technology 87 A
Human Resources 15 0.0980
Administrative B C
Total D 1.0000
Answer the following questions:
a) Compute A, B, C and D. (6 points)
b) Obtain an appropriate graphical representation of these data. (6 points)

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Q2

Question 2
A company manufactures and sells 30 different products, all of which require a specific manual operation before they are finished.
The following table lists the products, their price and the amount of time of manual labor required by each product.
Product Price [€] Manual labor [minutes]
#1 890 84
#2 1290 54
#3 429 28
#4 2390 180
#5 1990 92
#6 4590 391
#7 890 69
#8 849 83
#9 790 78
#10 3790 352
#11 2190 225
#12 1890 147
#13 1790 222
#14 1290 166
#15 1390 127
#16 769 102
#17 4890 572
#18 599 84
#19 869 123
#20 1490 166
#21 2090 280
#22 1790 209
#23 1299 119
#24 1199 166
#25 999 75
#26 1890 216
#27 1690 233
#28 799 50
#29 849 49
#30 3490 360
Answer the following questions:
a) Use an histogram to represent the distribution of the variable Price (you can do a stem and leaf plot if you prefer or cannot draw an histogram using your software). (6 points)
b) How would you classify this distribution in terms of skewness? (5 points)
c) Compute the mean, the median and the standard deviation of the variable Price. (6 points)
d) Compute the correlation coefficient between the two numerical variables, Price and Manual labor. How would you describe the relationship between these two variables. (5 points)
e) If you were asked to build a regression model, which of the two variables would you select as explanatory, and why? (5 points)
f) Based on your answer to the previous question, compute the coefficients of the linear regression model. (5 points)
g) Depending on your answer to question e), use your linear regression model to predict the value of Manual labor for a product with a price of 4000€, or the value of Price for a product with a Manual labor of 500 minutes. (5 points)
h) Obtain an appropriate graphical representation of the 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). (6 points)
i) This company wants to display its products in a trade fair, but due to space constraints, only six products can be displayed. Undecided, the manager decides to randomly select the products. How can he proceed to make sure the process is random and that six different products are selected? (6 points)

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Q3

Question 3
A sample of 40 insects of a certain species is used to measure the wingspan, in milimeters (variable X).
7.75 7.59 6.37 7.44 6.94 6.36 6.33 8.58
5.80 6.65 8.47 7.65 7.74 6.50 7.42 8.35
6.05 6.74 6.87 6.47 6.59 7.88 7.40 7.40
7.14 6.52 6.89 7.41 9.13 8.79 7.22 7.05
6.27 6.86 7.14 4.68 5.73 4.60 7.38 7.08
Answer the following questions:
a) Based on this sample, compute a confidence interval for the mean of X, for a confidence level of 95%. (8 points)
b) Assuming the standard deviation of the population is equal to the sample standard deviation, determine the sample size required for a confidence interval with a margin of error of 0.2 mm and a confidence level of 98%. (8 points)

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Q4

Question 4
A company that produces bicycle tires is testing the duration of the new, hopefully better version of its flagship product. The previous version lasted for an average of 3500 km. In order to evaluate the new tires, tests are carried out to a sample of 50 tires. Test results produce a sample average of 3863 km and a sample standard deviation of 482 km. For a significance level of 5%, can we conclude that the new tires can withstand more km than the previous version?
Answer the following questions:
a) Should a Z test for the mean or a t test for the mean be carried out? Justify your answer. (5 points)
b) Should this test for the mean be two-tailed, right-tailed or left-tailed? Justify your answer. (5 points)
c) State the null hypothesis and the alternative hypothesis. (5 points)
d) Perform the necessary computations to run this hypothesis test (you can use the rejection region method or the p-value method). 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. (8 points)

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Applied Management Statistics Resit Report Activity brief BCO127 Applied Management Statistics Online campus Professor: Paulo Azevedo | [email protected]

Description Several questions on the topics of variable description and graphical representation, normal distributions, correlation and data sampling, confidence intervals, regression and tests of hypothesis. Data and questions are provided below and in separate spreadsheet file (XLS).

Format You must submit a spreadsheet file with your answers (xlsx, ods). You can edit the “DATA” file with your answers and submit it if you wish, or use a separate file.

Goal(s) Test the students’ understanding of all the Applied Management Statistics topics.

Due date (RESIT SESSION)

Weight towards final grade

-

Learning outcomes

1. Understand concepts, formulas and techniques of statistics through exercises and applied examples; 2. Understand statistical language, statistical context, uncertainty, and develop statistical thinking; 3. Design statistical models, perform analysis, and solve real-world problems; 4. Interpret results of statistical analysis.

Assessment criteria

See the rubric below. Some relevant instructions:

• Graphs should be titled and the axes should be adequately labeled.

• Your file must be readable, and all answers must be identified by the question number.

• All the built-in functions (ex: AVERAGE()) must be included and visible – do not paste values computed elsewhere.

• A written explanation must be given when asked (ex: “Justify”).

Rubric

Task Between 90% and 100% Between 80% and 90% Between 60% and 80% Between 30% and 60% Between 0% and 30% Computation Result and process are correct,

and answer is well explained. Minor details may cause deduction of points.

Minor errors leading to wrong result, but explanation 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

Wrong result, lacking any coherent explanation.

Written answer

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, units and legends if needed)

Some minor readability or presentation.

Important incorrections, but graphs still conveys most relevant information.

Serious incorrections renderering the graph almost useless, but correct type of graph and variables are used.

No graphs is presented, or graph completely misses the graph (incorrect graph type and/or variables)

Questions and data

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