Question

a food safety guideline is that the mercury in fish should be below 1 part per million (ppm). listed below are the amounts of mercury (ppm) found in tuna sushi sam stores in a major city. construct a 90% confidence interval estimate of the mean amount of mercury in the population. does it appear that there is too much mercur 0.55 0.81 0.10 0.97 1.30 0.49 0.82 what is the confidence interval estimate of the population mean μ? 0.438 ppm < μ < 1.002 ppm (round to three decimal places as needed.) does it appear that there is too much mercury in tuna sushi? oa. yes, because it is possible that the mean is greater than 1 ppm. also, at least one of the sample values exceeds 1 ppm, so at least some of the fish have too much m ob. yes, because it is possible that the mean is not greater than 1 ppm. also, at least one of the sample values exceeds 1 ppm, so at least some of the fish have too much mercury. oc. no, because it is possible that the mean is not greater than 1 ppm. also, at least one of the sample values is less than 1 ppm, so at least some of the fish are safe. od. no, because it is not possible that the mean is greater than 1 ppm. also, at least one of the sample values is less than 1 ppm, so at least some of the fish are safe.

Explanation:

A confidence interval gives a range of values within which the population parameter (here, the mean amount of mercury) is likely to lie. The 90% confidence interval is \(0.438\) ppm \(<\mu<1.002\) ppm. This means that there is a 90% chance that the true population mean of mercury in tuna sushi is within this interval. Since the upper limit of the confidence interval (\(1.002\) ppm) is very close to \(1\) ppm (the safety guideline), it is still possible that the mean is not greater than \(1\) ppm. Just because one sample value (\(1.30\) ppm) exceeds \(1\) ppm does not necessarily mean the entire population (all tuna sushi in the stores) has too much mercury. We make inferences about the population mean from the confidence interval for the mean, not from individual sample values when answering if there is "too much" mercury (as the guideline is about the amount in fish in general, which relates to the population mean).

Answer:

C. No, because it is possible that the mean is not greater than 1 ppm. Also, at least one of the sample values exceeds 1 ppm, so at least some of the fish have too much mercury.