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 90​% 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, 0.71, 0.10, 0.93, 1.33, 0.58, 0.94

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 = 0.7429
sample standard deviation, s = 0.3823
sample size, n = 7
degrees of freedom, df = n - 1 = 6

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 1.943

ME = tc * s/sqrt(n)
ME = 1.943 * 0.3823/sqrt(7)
ME = 0.281

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (0.7429 - 1.943 * 0.3823/sqrt(7) , 0.7429 + 1.943 * 0.3823/sqrt(7))
CI = (0.46 , 1.02)