Question

PLEASE SHOW ALL WORKING SOLUTION.

6. 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. You obtain research funding to randomly sample 32 landscapers, collect blood samples, and send these samples to your collaborating lab in order to quantify the amount of vitamin D in the landscapers' 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 table.

Subject	Vitamin D
1	52.302
2	49.759
3	48.600
4	54.250
5	54.471
6	44.368
7	59.069
8	39.274
9	51.450
10	52.775
11	43.932
12	38.869
13	46.883
14	47.327
15	42.138
16	54.582
17	51.237
18	48.288
19	51.549
20	54.153
21	47.296
22	51.199
23	43.553
24	44.872
25	46.279
26	61.316
27	37.778
28	50.675
29	51.426
30	57.838
31	43.750
32	45.827

What is the estimated 95% confidence interval (CI) of the average blood vitamin D level of US landscapers in ng/mL?

Please note the following: 1) 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; 2) ensure you use either the large or small sample CI formula as appropriate; and 3) you may copy and paste the data into Excel to facilitate analysis.

Select one:

a. 47.0 to 51.0 ng/mL

b. 42.3 to 47.4 ng/mL

c. 39.5 to 45.4 ng/mL

d. 42.0 to 57.3 ng/mL

Answer 1

Following is the output of descritpive statstics:

Correct option is

a. 47.0 to 51.0 ng/mL

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Since sample size is greater than 30 and it is given that population is normally distributed so we can use z interval as follow:

Using above:

Correct option is

a. 47.0 to 51.0 ng/mL