Question

A food safety guideline is that mercury in fish should be below 1 part per million (ppm). Listed below are the amounts of mecury (ppm) found in tuna sushi samples at different stores in a major city. construct a 95% confidence interval estimate of the mean of the mass amount of mercury in the population. Does it appear that there is too much mercury in tuna sushi?

0.53 074 0.10 0.95 1.20 0.53 0.90

Answer 1

Constructing a 95% confidence interval for the mean amount of mercury in tuna sushi involves calculating the sample mean, standard deviation, finding the appropriate t-value, and using these to compute the margin of error and the interval itself. If the interval exceeds 1 ppm, it could indicate a potential health risk.

Step-by-step explanation:

To construct a 95% confidence interval estimate of the mean amount of mercury in tuna sushi, we need to first compute the sample mean (μ) and the standard deviation (s) from the provided data. Then we can use the t-distribution since the sample size is small and we assume the population standard deviation is unknown.

The provided mercury levels in ppm are: 0.53, 0.74, 0.10, 0.95, 1.20, 0.53, 0.90.

1. Calculate the sample mean (μ): (μ = (0.53 + 0.74 + 0.10 + 0.95 + 1.20 + 0.53 + 0.90) / 7).
2. Calculate the sample standard deviation (s).
3. Find the t-value for a 95% confidence interval with 6 degrees of freedom (n-1).
4. Calculate the margin of error (ME) using the formula: ME = t * (s / √(n)).
5. The confidence interval is then μ ± ME.

After calculation, if the interval exceeds 1 ppm, it would indicate that the mean level of mercury could be concerning according to the food safety guidelines.