Applied Management Statistics

AMS_Resit_A_DATA.xlsx

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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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