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 $95 \%$ confidence interval estimate of the mean amount of mercury in the population. Does it appear that there is too much mercury in tuna sushi?
\[
0.55 \quad 0.78 \quad 0.11 \quad 0.88 \quad 1.27 \quad 0.57 \quad 0.96 \quad \text { 무 }
\]
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 mercury levels in ppm are: 0.55, 0.78, 0.11, 0.88, 1.27, 0.57, 0.96.

Step 2 ：Calculate the sample mean \(\bar{x}\) by adding all the values and dividing by the number of values. The sample mean \(\bar{x}\) is approximately 0.731.

Step 3 ：Calculate the sample standard deviation \(s\) using the formula for standard deviation. The sample standard deviation \(s\) is approximately 0.368.

Step 4 ：The sample size \(n\) is the number of values, which is 7.

Step 5 ：Substitute these values into the formula for a confidence interval: \(\bar{x} \pm z \frac{s}{\sqrt{n}}\). The z-score \(z\) for a 95% confidence interval is 1.96.

Step 6 ：Calculate the confidence interval, which is approximately (0.459, 1.004).

Step 7 ：\(\boxed{\text{Final Answer: The 95% confidence interval estimate of the population mean } \mu \text{ is } 0.459 \, \text{ppm} < \mu < 1.004 \, \text{ppm}.}\) This means we are 95% confident that the true mean amount of mercury in the population is between 0.459 ppm and 1.004 ppm. Since the upper limit of the confidence interval is above 1 ppm, it appears that there might be too much mercury in tuna sushi. However, further testing would be needed to confirm this.