Question

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?

0.58    0.80    0.09 0.95    1.32    0.59 0.96   
What is the confidence interval estimate of the population mean μ​?

_____ppm<μ<_____ppm (Round to 3 Decimal places as needed)

Does it appear that there is too much mercury in tuna​ sushi?

Answer 1

For the data given, we have the following descriptive statistics calculated using a statistics tool:

Sample size, n = 7

Sample mean, m = 0.76

Sample standard deviation, S = 0.388

Degrees of freedom, df = n-1 = 6

Standard error of mean, SE = S/(n^0.5) = 0.388/(6^0.5) = 0.158

For a 98% confidence interval, the critical t-value with df = 6 is:

t_c = 3.14

So, the 98% CI is as follows:

m - (tc*SE) < μ < m + (tc*SE)

Put the respective values:

0.76 - (3.14*0.158) < μ < 0.76 + (3.14*0.158)

0.263 < μ < 1.256

Since this interval also contains the values above 1, so we can say that it appears that there is too much mercury in tuna sushi.