Problem 16-9 The air quality in a building is of interest to an environmental en

Question

Problem 16-9

The air quality in a building is of interest to an environmental engineer. The mean air quality is measured in the form of the amount of pollutant in the air in parts per million (ppm). The mean amount of pollutant can be assumed to have a normal probability distribution with a mean (mu) and standard deviation (sigma). The standard deviation of pollutant (sigma) is known to be 0.2 ppm. The air quality based on the records of the building has a mean of 3 ppm and a standard deviation of 0.2 ppm. A sample of n = 10 was collected. The sample resulted in a mean of 2.7 ppm. Determine: (a) the posterior mean pollutant concentration. (b) the posterior standard deviation, and (c) the 95% confidence intervals for the mean concentration based on prior and posterior information.

Explanation / Answer

a.
Mean=3ppm
b.
standard deviation=o.2 ppm
c.
Confidence Interval
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=3
Standard deviation( sd )=0.2
Sample Size(n)=10
Confidence Interval = [ 3 ± Z a/2 ( 0.2/ Sqrt ( 10) ) ]
= [ 3 - 1.96 * (0.06) , 3 + 1.96 * (0.06) ]
= [ 2.88,3.12 ]

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