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 sampled 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? \[ \begin{array}{lllllll} 0.60 & 0.83 & 0.11 & 0.94 & 1.34 & 0.50 & 0.85 \end{array} \] What is the confidence interval estimate of the population mean $\mu$ ? $\mathrm{ppm}<\mu<\square \mathrm{ppm}$ (Round to three decimal places as needed.)

Step 1 ：Given the data of mercury levels in tuna sushi from different stores in a major city, we are asked to construct a 99% confidence interval estimate of the mean amount of mercury in the population and determine if there is too much mercury in tuna sushi. The data is as follows: \[0.60, 0.83, 0.11, 0.94, 1.34, 0.50, 0.85\] ppm.

Step 2 ：First, we calculate the sample size, which is the number of data points. In this case, the sample size (n) is 7.

Step 3 ：Next, we calculate the sample mean, which is the sum of all data points divided by the sample size. The sample mean is approximately \(0.739\) ppm.

Step 4 ：Then, we calculate the sample standard deviation, which measures the amount of variation or dispersion of a set of values. The sample standard deviation is approximately \(0.386\) ppm.

Step 5 ：We also need to find the z-score for a 99% confidence level. The z-score is a measure of how many standard deviations an element is from the mean. The z-score for a 99% confidence level is approximately \(2.576\).

Step 6 ：Using these values, we can calculate the confidence interval. The lower limit of the confidence interval is calculated as the sample mean minus the z-score times the standard deviation divided by the square root of the sample size. The upper limit is calculated as the sample mean plus the z-score times the standard deviation divided by the square root of the sample size. The confidence interval is approximately \(0.363\) ppm to \(1.114\) ppm.

Step 7 ：\(\boxed{\text{Final Answer: The 99% confidence interval estimate of the population mean } \mu \text{ is } 0.363 \, \text{ppm}<\mu<1.114 \, \text{ppm}.}\)