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I am interested in looking at the salaries of professors to see if they are cons

ID: 468854 • Letter: I

Question

I am interested in looking at the salaries of professors to see if they are consistently paid similarly, regardless of location and specialties. Random samples of size four were taken and produced the following data:

Sample

Average

Range

1

95751.6

33196

2

74659.8

19028

3

64632.2

17445

4

64964

18169

5

88361.6

29142

6

73477.4

16012

7

63611.4

11595

8

64352

14901

                a. Find the UCL for the R chart.

                b. Find the LCL for the R chart.

                c. Is this chart in control? Why/why not?

                d. Find the UCL for the -chart.

                e. Find the LCL for the -chart.

                f. Is this process in control? Why/why not?

Sample

Average

Range

1

95751.6

33196

2

74659.8

19028

3

64632.2

17445

4

64964

18169

5

88361.6

29142

6

73477.4

16012

7

63611.4

11595

8

64352

14901

Explanation / Answer

1. UCL = D4*R

where R is the average range = Sum of all ranges/8 = 19936

D4 = 1.864 (from the table)

UCL = 1.864*19936 = 37160

2. LCL = D3*R

D3 = 0.136

So, LCL = 0.136*19936 = 2711