Listed below are measured amounts of lead (in micrograms per cubic meter, or mu

Question

Listed below are measured amounts of lead (in micrograms per cubic meter, or mu g/m^3) in the air. The EPA has established an air quality standard for lead of 1.5 pg/m^3. The measurements shown below were recorded at a building on different days. Use the given values to construct a 95% confidence interval estimate of the mean amount of lead in the air. Is there anything about this data set suggesting that the confidence interval might not be very good? What is the confidence interval for the population mean mu? mu g/m^3

Explanation / Answer

CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=1.646
Standard deviation( sd )=2.1077
Sample Size(n)=5
Confidence Interval = [ 1.646 ± t a/2 ( 2.1077/ Sqrt ( 5) ) ]
= [ 1.646 - 2.776 * (0.943) , 1.646 + 2.776 * (0.943) ]
= [ -0.971,4.263 ]

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