An artide considered various issues associated with determining endotoxin concen

Question

An artide considered various issues associated with determining endotoxin concentration. The following data on concentration (EU/mg) In settled dust for one sample of urban homes and another of farm homes was kindly supplied by the authors of the article. U:6.0 s.0 11.0 33.0 4.0 S.0 82.0 18.0 35.0 17.0 23.0 F:4.0 14.0 10 9.0 9.0 8.0 4.0 20.0 s.0 8.9 21.0 9.2 3.0 2.0 0.3 (a) Determine the value of the sample standard deviation for each sample. Hint: x-239.0 for the urban sample and 128.4 for the farm sample, and x,2-10,403 for the urban sample and 1617.94 or the rm sample Round your answers to two decimal places.) rban-settings farm-settiing Interpret these values.

Explanation / Answer

Solution:

Here, we have to calculate the sample standard deviations for the two data sets for urban-setting and farm-setting. The formula for sample standard deviation is given as below:

S = sqrt[(X2 – (X)2/n )/(n – 1)]

For urban-setting data, we are given

X = 239

X2 = 10403

n = 11

S = sqrt[(10403 – 239^2/11)/(11 – 1)]

S = sqrt[(10403 – 239^2/11)/10]

S = sqrt[(10403 – 5192.818)/10]

S = sqrt[5210.182/10]

S = sqrt(521.0182)

S = 22.82582

For Farm-setting data, we are given

X = 128.4

X2 = 1617.94

n = 15

S = sqrt[(1617.94 – 128.4^2/15)/(15 – 1)]

S = sqrt[(1617.94 – 128.4^2/15)/14]

S = sqrt[(1617.94 – 16486.56/15)/14]

S = sqrt[(1617.94 – 1099.104)/14]

S = sqrt[518.836/14]

S = sqrt(37.05971)

S = 6.087669

Answers:

Urban-setting: S = 22.83

Farm-setting: S = 6.09

Data for urban setting have more variation than the data for farm setting.

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