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BCO127

APPLIED MANAGEMENT STATISTICS Timed Exercise 2-Task brief & rubrics.

Task

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Individual task.

Students are required to answer all the questions.

Time: 2 hours to complete the exercise.

QUESTIONS:

A process is making plastic parts with a diameter specification of 25+0.5 mm.

Some problems of quality are happening. The production manager is thinking that the temperature is a factor that affects to manufacturing.

A random sample of 12 units is taken. The temperature and the results for each are:

Sample

Temperature (ºC)

Specification (mm)

1.

2.

3.

4.

5.

6.

1

20

24.9

2

15

24.6

3

18

24.8

4

24

25.4

5

22

25.1

6

13

24.5

7

21

25.1

8

23

25.2

9

17

24.7

10

19

25

11

20

25

12

16

24.7

Plot a scatter diagram of the data. (10 points)

Calculate the linear regression equation that best fits the data. Calculate the factors a and b step by step and by Excel. (10 points)

Explain what is the meaning of a correlation coefficient (r)? (10 points)

Calculate the correlation coefficient (r) step by step and by Excel and determine what is the type of correlation between these variables. (10 points)

Estimate the specification when temperature is 16.5 ºC, 25ºC and 27ºC. (15 points)

What is the temperature that gives the optimal specification? (10 points)

The manager believes that the process is making parts shorter than usual. The following table shows all the production of the last hour (a population of 49 units):

01

02

03

04

05

06

07

25

24.9

24.8

25

24.7

24.9

25

08

09

10

11

12

13

14

25.2

24.8

24.7

25

24.9

25.2

24.8

15

16

17

18

19

20

21

25

24.9

25

25.1

24.8

25

24.7

22

23

24

25

26

27

28

25.1

24.7

24.6

25

24.9

24.7

25.1

29

30

31

32

33

34

35

25

24.9

24.8

24.7

25

25.3

24.9

36

37

38

39

40

41

42

25.2

24.6

25.1

25

24.8

24.9

25

43

44

45

46

47

48

49

25

24.8

25.1

25

24.9

25

24.8

7. Choose a random sample of 15 units using the Table of Random Numbers. Show how the sample is chosen. (15 points)

8. Calculate the arithmetic mean, the mode and the median of the sample and determine if the manager’s belief is correct. (10 points)

9. Draw the histogram of the population data and confirm your answer in question 8. (10 points)

Formalities:

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Wordcount: 1000 words.

Cover, Table of Contents, References and Appendix are excluded of the total wordcount.

Font: Arial 12,5 pts.

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