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 divided by m cubedg/m3) in the air. The EPA has established an air quality standard for lead of 1.5 mu g divided by m cubedg/m3. 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? 5.40, .90, .34, .79, .69, .90

Explanation / Answer

we can quickly analyse this in the open source statistical package R

we know that the confidence interval is given as

mean +- z*SD/sqrt(n)

The R snippet is

> points <- c(5.40, .90, .34, .79, .69, .90)
>
> ## upper limit
> mean(points) + qnorm(1-0.05/2)*sd(points)/sqrt(length(points))
[1] 3.039781
>
> ## lower limit
>
> mean(points) - qnorm(1-0.05/2)*sd(points)/sqrt(length(points))
[1] -0.03311398

So the confidence interval is

-0.033 , 3.03

this means that we are 95% sure that the true mean would lie in this range , however we see that the lower limit as low as zero and as high as 3, hence we cant be sure if it would be close to 1.5 or not

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