A food safety guideline is that the mercury in fish should be below 1 part per million​ (ppm).

Question

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?

0.56  0.79  0.10  0.94  1.36  0.54  0.87

What is the confidence interval estimate of the population mean mu​?

Answer 1

For a sample size of 7, we will compute the 98% confidence interval as follows:

mean +/- std dev/sqrt(7) * t critical for 98% CI and 6 DOF

The mean and std dev are 0.737 and 0.393, respectively.

t critical for 98% CI and 6 DOF is gotten from the t-table for tail probability 0.01 and 6 DOF = 3.143

so the 98% CI is 0.737 +/- 0.393/sqrt 7 * 3.143

0.737 +/- 0.148 * 3.143 = (0.272,1.202)

1 is among the plausible values for the true population ppm, so cannot conclude population mu < 1, however, only one of the 7 samples exceeds 1 ppm and the set of plausible values is centered around a value < 1.