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?

Mercury (ppm)
0.61, 0.70, 0.09, 0.91, 1.28, 0.55, 0.83

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

___ppm < μ <___ppm

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

Answer 1

sample mean, xbar = 0.71
sample standard deviation, s = 0.365
sample size, n = 7
degrees of freedom, df = n - 1 = 6

Given CI level is 98%, hence α = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01, tc = t(α/2, df) = 3.143

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (0.71 - 3.143 * 0.365/sqrt(7) , 0.71 + 3.143 * 0.365/sqrt(7))
CI = (0.2764 , 1.1436)

0.2764 < mu < 1.1436

As the CI included 1 ppm, there is not sufficient evidence to conclude that the mean amount of mercury is less than 1 ppm. Hence there is too much mercury in tunasushi