Listed below are measured amounts of lead in micrograms per

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 mug / m^3 The measurements shown below were recorded at a budding 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? Is there anything about this data set suggesting that the confidence interval might not be very good?

Solution

a)

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    1.588333333          
t(alpha/2) = critical t for the confidence interval =    2.570581836          
s = sample standard deviation =    1.888665314          
n = sample size =    6          
df = n - 1 =    5          
Thus,              
              
Lower bound =    -0.393699359          
Upper bound =    3.570366025          
              
Thus, the confidence interval is              
              
(   -0.393699359   ,   3.570366025   ) [ANSWER]

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b)

D. Yes, the value 5.40 appears to be an outlier. [ANSWER]

This is a problem because we are assuming that the population is approximately normally distributed to use the t distrbution here.