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 47 landscapers and 38 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 47.254 2 45.598 3 42.718 4 56.459 5 51.924 6 58.933 7 53.588 8 49.171 9 59.213 10 47.921 11 56.453 12 52.928 13 43.992 14 52.561 15 48.098 16 49.735 17 49.588 18 48.375 19 52.636 20 49.012 21 54.467 22 53.818 23 50.668 24 55.031 25 48.707 26 52.340 27 58.508 28 48.444 29 45.857 30 51.929 31 51.685 32 45.187 33 51.246 34 51.127 35 52.814 36 44.682 37 52.031 38 49.119 39 51.202 40 54.415 41 53.461 42 49.713 43 47.263 44 52.518 45 53.049 46 44.160 47 49.453 Table 2. Office Workers Subject Vitamin D 1 46.070 2 46.412 3 48.284 4 47.721 5 51.647 6 48.276 7 43.860 8 53.975 9 41.098 10 48.023 11 49.179 12 47.082 13 50.054 14 49.036 15 53.273 16 42.339 17 50.070 18 42.391 19 51.898 20 54.916 21 42.022 22 42.387 23 41.010 24 43.888 25 44.560 26 44.624 27 50.100 28 45.727 29 40.750 30 41.952 31 41.738 32 38.903 33 48.609 34 49.119 35 47.827 36 38.487 37 44.227 38 42.965 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. 2.92 to 6.40 ng/mL b. 3.12 to 7.36 ng/mL c. 3.20 to 7.20 ng/mL d. 2.60 to 6.91 ng/mL

Answer 1

Group1=(47.254, 45.598, 342.718, 56.459, 51.924, 58.933, 53.588, 49.171, 59.213, 47.921, 56.453, 52.928, 43.992, 52.561, 48.098, 49.735,49.588,48.375, 52.636,49.012,54.467,53.818, 50.668, 55.031, 48.707,52.340, 58.508,48.444,45.857,51.929,51.685,45.187,51.246,51.127,52.814,44.682,52.031,49.119,51.202,54.415,53.461, 49.713,47.263,52.518,53.049,44.160,49.453)

Group2=(46.070, 46.412,48.284,47.721,51.647,48.276,43.860,53.975,41.098,48.023,49.179,47.082,50.054, 49.036,53.273,42.339 ,50.070,42.391, 51.898, 54.916, 42.022,42.387,41.010,43.888 , 44.560, 44.624, 50.100, 45.727, 40.750,41.952, 41.738,38.903,48.609, 49.119,47.827, 38.487, 44.227,42.965)

Group1=Landscapers Subject Vitamin D, Group 2=Office Workers Subject Vitamin D