Question 10 of 12 This quize 12 point(s) possible This question: 1 point(e) possible Submit quiz 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 funa sushi samplod at different stores in a major city. Construct a $99 \%$ confidence interval estimate of the mean amount of mercury in the population. Does it appear that there is too much mercury in tuna sushi? \[ \begin{array}{llllllllll} 0.61 & 0.81 & 0.09 & 0.94 & 1.33 & 0.52 & 0.92 \end{array} \] What is the confidence intorval estimate of the population mean $\mu$ ? $\square \mathrm{ppm}<\mu<\square \mathrm{ppm}$ (Round to three decimal places as needed.) Does it appear that there is too much mercury in tuna sushi? A. Yes, because it is possible that the mean is greater than $1 \mathrm{ppm}$. Also, at least one of the sample values exceeds 1 ppm, so at least some of the fish have too much mercury. B. 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. C. 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. D. Yes, because it is possible that the mean is not greater than $1 \mathrm{ppm}$. Also, at least one of the sample values exceeds 1 ppm, so at least some of the fish have too much mercury. Next
Solution
Step 1 ：Calculate the mean and standard deviation of the given data. The data is [0.61, 0.81, 0.09, 0.94, 1.33, 0.52, 0.92]. The mean is approximately \(0.746\) and the standard deviation is approximately \(0.361\).
Step 2 ：Calculate the 99% confidence interval for the mean amount of mercury in the population using the formula \(\bar{x} \pm z \frac{s}{\sqrt{n}}\), where \(\bar{x}\) is the sample mean, \(z\) is the z-score corresponding to the desired confidence level (for a 99% confidence interval, \(z \approx 2.576\)), \(s\) is the sample standard deviation, and \(n\) is the sample size. The margin of error is approximately \(0.352\).
Step 3 ：The confidence interval for the mean amount of mercury in the population is approximately \((0.394, 1.097)\) ppm. This means that we are 99% confident that the true mean amount of mercury in the population is between \(0.394\) ppm and \(1.097\) ppm.
Step 4 ：Compare the confidence interval to the safety guideline of 1 ppm. Since the upper limit of the confidence interval (\(1.097\) ppm) is greater than the safety guideline of 1 ppm, it is possible that the mean amount of mercury in the population is greater than 1 ppm. Also, at least one of the sample values (\(1.33\) ppm) exceeds 1 ppm, so at least some of the fish have too much mercury.
Step 5 ：Final Answer: The confidence interval estimate of the population mean \(\mu\) is \(0.394 \mathrm{ppm}<\mu<1.097 \mathrm{ppm}\). It appears that there is too much mercury in tuna sushi because it is possible that the mean is greater than \(1 \mathrm{ppm}\). Also, at least one of the sample values exceeds 1 ppm, so at least some of the fish have too much mercury. So, the answer is \(\boxed{\text{A. Yes, because it is possible that the mean is greater than } 1 \mathrm{ppm}. \text{Also, at least one of the sample values exceeds 1 ppm, so at least some of the fish have too much mercury.}}\)
