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? 0.54  0.73  0.10  0.93  1.33  0.59  0.84

What is the confidence interval estimate of the population mean mu​? ​(Round to three decimal places as​ needed.)

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

A. ​No, because it is not possible that the mean is greater than 1 ppm.​ Also, at least one of the sample values is less than 1​ ppm, so at least some of the fish are safe.

B. ​Yes, because it is possible that the mean is not greater than 1 ppm.​ Also, at least one of the sample values exceeds 1​ ppm, so at least some of the fish have too much mercury.

C. ​No, because it is possible that the mean is not greater than 1 ppm.​ Also, at least one of the sample values is less than 1​ ppm, so at least some of the fish are safe.

D. ​Yes, because it is possible that the mean is greater than 1 ppm.​ Also, at least one of the sample values exceeds 1​ ppm, so at least some of the fish have too much mercury.

Answer 1

The mean of the sample data is calculed using Excel as 0.722857 and sample standard deviation as 0.379549 so,

The formula for estimation is:

μ = M ± t(s_M)

where:

M = sample mean
t = t statistic determined by confidence level
s_M = standard error = √(s²/n)

M = 0.72286
t = 3.71
s_M = √(0.379549²/7) = 0.14

μ = M ± t(s_M)
μ = 0.72286 ± 3.71*0.14
μ = 0.72286 ± 0.5318529

99% CI [0.191, 1.255].

So,

D. ​Yes, because it is possible that the mean is greater than 1 ppm.​ Also, at least one of the sample values exceeds 1​ ppm, so at least some of the fish have too much mercury.

The T-table used for t-distribution t statistic calculation is