Question

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Researchers interested in lead exposure due to car exhaust sampled the blood of 52 road construction workers subjected to constant inhalation of automobile exhaust fumes while working downtown in a city. The blood samples of these workers had an average lead concentration of 124.32 μg/l and a SD of 37.74 μg/l; a previous study of people from a nearby suburb, with no history of exposure, found an average blood level concentration of 35 μg/l.

a. Write down the hypotheses that would be appropriate for testing if the construction workers appear to have been exposed to a higher concentration of lead.

b.​​​​​​​ Explicitly state and check all conditions necessary for inference on these data.

c. ​​​​​​​​​​​​​​Test the hypothesis that the downtown construction workers have a higher lead exposure than the group in the previous study. Interpret your results in context.

Answer 1

Solution - from the Given data, Sample size (n ) = 52 Sample mean (a)= 124.32 Mgll Sample standard deviation (S) = 37.74 Mg/L null hypothesis Hoius 35 alternative hypothesis: H:4> 35 b) Here they have given the sample standard deviation, not the population Standard deviation therefore we cannot 7 - Test here to apply Test-t either one of the above condition should saristy * the population should be normal * Sample size should be greater than 30 we have the sample size 52, that means greater than 30, so we. can apply t-test Co test statistic, will be t=a-M 124:32-35 $10 37074/552 170066 P-value Degree of freedom (n-1) 52-1 - 51 t( 19.066, 519 = 0.000016 ere 'p' value is 0.00001). Interpretation Since Pt is very small (P-value) it is highly significant to reject the null hypothesi's Hence it as concluded that police officers have higher lead exposure than the group in the previous study