Questions: 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 98% confidence interval estimate of the mean amount of mercury in the population. Does it appear that there is too much mercury in tuna sushi? 0.54, 0.78, 0.11, 0.97, 1.35, 0.51, 0.80 What is the confidence interval estimate of the population mean μ ? ppm < μ < ppm (Round to three decimal places as needed.)

Solution Steps

The mean mercury level in the sampled tuna sushi is calculated as follows:

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} = \frac{5.06}{7} = 0.723 \text{ ppm} \]

The sample standard deviation of the mercury levels is determined to be:

\[ s = 0.391 \text{ ppm} \]

For a 98% confidence level, the Z-score is:

\[ Z = 2.326 \]

The margin of error is calculated using the formula:

\[ \text{Margin of Error} = \frac{Z \times s}{\sqrt{n}} = \frac{2.326 \times 0.391}{\sqrt{7}} \approx 0.344 \text{ ppm} \]

The 98% confidence interval for the mean amount of mercury is given by:

\[ \text{Confidence Interval} = \left( \mu - \text{Margin of Error}, \mu + \text{Margin of Error} \right) = \left( 0.723 - 0.344, 0.723 + 0.344 \right) = (0.379, 1.067) \text{ ppm} \]

Since the upper limit of the confidence interval is \(1.067\) ppm, which is above the safety guideline of \(1\) ppm, we conclude that:

The mercury level in tuna sushi is within the safe limit.

Final Answer