Question

Researchers interested in lead exposure due to car exhaust sampled the blood of 52 police officers subjected to constant inhalation of automobile exhaust fumes while working traffic enforcement in a primarily urban environment. The blood samples of these officers had an average lead concentration of 48.32 μg/l and standard deviation of 37.74 μg/l; a previous study of individuals from a nearby suburb, with no history of exposure, found an average blood level concentration of 35 μg/l. (8 points) Test the hypothesis that the downtown police officers have a higher lead exposure than the group in the previous study (higher than 35 μg/l) at 1% significance level. [Follow the 5-step]

Answer 1

given data are:-

sample mean () = 48.32

sample sd(s) = 37.74

sample size(n) = 52

hypothesis:-

(claim)

here, as the sample sd is known and sample size is large enough we will do 1 sample t test for mean.

test statistic is -

df = (n-1) = (52-1) = 51

the p value is :-

[ in any blank cell of excel type =T.DIST.RT(2.545,51)]

decision:-

p value = 0.007 < 0.01 (alpha)

so, we reject the null hypothesis.

conclusion:-

there is sufficient evidence to support that the downtown police officers have a higher lead exposure than the group in the previous study at 1% significance level.

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