Question

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 36 landscapers and 45 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	58.839
2	52.282
3	54.337
4	55.843
5	60.780
6	54.857
7	62.282
8	40.105
9	59.074
10	55.160
11	51.987
12	54.314
13	54.888
14	53.734
15	56.989
16	48.595
17	54.399
18	52.009
19	50.950
20	53.560
21	54.749
22	59.856
23	49.503
24	54.571
25	52.041
26	65.108
27	51.093
28	50.234
29	57.178
30	44.838
31	57.767
32	52.131
33	44.144
34	54.469
35	55.968
36	53.619

Table 2 - Office Workers

Subject	Vitamin D
1	43.898
2	44.372
3	47.292
4	43.896
5	47.256
6	44.187
7	44.452
8	40.937
9	53.387
10	48.877
11	41.475
12	60.245
13	47.933
14	34.593
15	42.342
16	47.129
17	45.068
18	42.113
19	36.233
20	46.898
21	47.185
22	41.505
23	44.729
24	44.721
25	44.964
26	39.215
27	48.520
28	43.410
29	42.867
30	51.610
31	42.815
32	40.480
33	51.219
34	44.407
35	36.975
36	40.645
37	44.995
38	43.638
39	41.939
40	42.065
41	60.411
42	51.144
43	37.382
44	51.664
45	50.755

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. 6.53 to 11.06 ng/mL

b. 6.08 to 12.72 ng/mL

c. 6.01 to 10.40 ng/mL

d. 6.96 to 12.23 ng/mL

Answer 1