Studies show that the concentration of PCBs is much higher...

Studies show that the concentration of PCBs is much higher in malignant breast tissue than in normal breast tissue. If a study of 50 women with breast cancer reveals an average PCB concentration of $22.8 \times 10^{-4}$ gram, with a standard deviation of $4.8 \times 10^{-4}$ gram, is the mean concentration of PCBs less than $24 \times 10^{-4}$ gram?

Perfluorooctanoic acid (PFOA) is a chemical used in products that coat cookware to prevent food from sticking. An agency is investigating the potential risk of PFOA as a cancer-causing agent. It is known that the blood concentration of PFOA in the general population has a mean of μ = 6 parts per billion (ppb) and a standard deviation of σ = 10 ppb. An article reported on tests for PFOA exposure conducted on a sample of 323 people who live near a factory that makes one such nonstick cookware product. a) What is the probability that the average blood concentration of PFOA in the sample is greater than 7.5 ppb? b) The actual study resulted in x̄ = 300 ppb. Use this information to make an inference about the true mean (μ) PFOA concentration for the population that lives near the factory.

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