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PLEASE SHOW ALL WORKING STEPS. THANKS 8. Recall in our discussion of the normal distribution the...

PLEASE SHOW ALL WORKING STEPS. THANKS

8. Recall in our discussion of the normal distribution the research study that examined the blood vitamin D levels of the entire US population of landscape gardeners. The intent of this large-scale and comprehensive study was to characterize fully this population of landscapers as normally distributed with a corresponding population mean and standard deviation, which were determined from the data collection of the entire population.

Suppose you are now in a different reality in which this study never took place though you are still interested in studying the average vitamin D levels of US landscapers. In other words, the underlying population mean and standard deviation are now unknown to you. Furthermore, you would like to collect data from US office workers to examine the difference between the average vitamin D levels of landscapers and office workers, which will reflect any occupational sun exposure differences as measured by blood vitamin D levels. You obtain research funding to sample at random 30 landscapers and 50 office workers, collect blood samples, and send these samples to your collaborating lab in order to quantify the amount of vitamin D in both groups' blood. After anxiously awaiting your colleagues to complete their lab quantification protocol, they email you the following vitamin D level data as shown in the following tables.

Table 1. Landscapers

Subject

Vitamin D

1

52.732

2

55.072

3

49.285

4

53.121

5

50.824

6

50.681

7

58.735

8

58.919

9

55.206

10

50.427

11

56.894

12

53.921

13

56.994

14

52.553

15

52.844

16

59.129

17

51.895

18

52.775

19

43.229

20

44.138

21

48.417

22

48.871

23

57.559

24

56.529

25

54.408

26

64.301

27

51.168

28

46.713

29

47.306

30

49.357

Table 2. Office Workers

Subject

Vitamin D

1

33.588

2

29.509

3

41.073

4

31.099

5

34.916

6

35.989

7

38.288

8

33.433

9

36.057

10

32.349

11

31.597

12

27.334

13

26.669

14

27.254

15

28.483

16

28.601

17

27.722

18

28.376

19

28.135

20

37.940

21

28.275

22

41.984

23

38.529

24

36.131

25

30.104

26

36.741

27

36.456

28

32.489

29

25.914

30

28.119

31

29.942

32

31.745

33

36.530

34

32.565

35

28.298

36

32.281

37

35.371

38

26.921

39

36.623

40

31.120

41

27.441

42

23.342

43

28.873

44

29.357

45

27.941

46

32.926

47

32.529

48

35.324

49

30.805

50

35.566

What is the estimated 95% confidence interval (CI) of the average difference in blood vitamin D levels between US landscapers and office workers in ng/mL? Assign groups 1 and 2 to be landscapers and office workers, respectively.

Please note the following: 1) in practice, you as the analyst decide how to assign groups 1 and 2 and subsequently interpret the results appropriately in the context of the data, though for the purposes of this exercise the groups are assigned for you; 2) you might calculate a CI that is different from any of the multiple choice options listed below due to rounding differences, therefore select the closest match; 3) ensure you use either the large or small sample CI formula as appropriate; and 4) you may copy and paste the data into Excel to facilitate analysis.

Select one:

a. 17.32 to 25.79 ng/mL

b. 20.99 to 25.68 ng/mL

c. 18.83 to 22.82 ng/mL

d. 20.15 to 26.25 ng/mL

Homework Answers

Answer #1

c. 18.83 to 22.82 ng/mL

The formula is:

The output is:

Landscapers Office Workers
52.80010 31.97308 mean
4.70179 4.23284 std. dev.
30 50 n
78 df
20.83 difference (Landscapers - Office Workers)
19.47 pooled variance
4.41 pooled std. dev.
1.02 standard error of difference
18.83 confidence interval 95.% lower
22.82 confidence interval 95.% upper
2.03 margin of error
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