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 99% confidence interval estimate of the mean amount of mercury in the population. Does it appear that there is too much mercury in tuna sushi?

0.62 , 0.76 , 0.10 , 0.94 , 1.38 , 0.51 , 0.95

Answer 1

Mean X̅ = Σ Xi / n
X̅ = 5.26 / 7 = 0.7514
Sample Standard deviation SX = √ ( (Xi - X̅ )2 / n - 1 )
SX = √ ( 0.9701 / 7 -1 ) = 0.4021

Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.01 /2, 7- 1 ) = 3.707
0.7514 ± t(0.01/2, 7 -1) * 0.4021/√(7)
Lower Limit = 0.7514 - t(0.01/2, 7 -1) 0.4021/√(7)
Lower Limit = 0.188
Upper Limit = 0.7514 + t(0.01/2, 7 -1) 0.4021/√(7)
Upper Limit = 1.3148
99% Confidence interval is ( 0.188 , 1.3148 )

Since the upper limit of confidence interval is greater than 1, hence we conlude that there is too much mercury in tuna sushi.