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?

0.62  

0.69  

0.11  

0.96  

1.25  

0.55  

0.85

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

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

A.

​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.

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.

​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.

Answer 1

We have to construct 98% confidence interval of estimate of the mean amount of mercury in the population.

Confidence interval for population mean is -

Obervation table -

Sr. No.	X	(X-x_bar)^2
1	0.62	0.0097
2	0.69	0.0008
3	0.11	0.3704
4	0.96	0.0583
5	1.25	0.2824
6	0.55	0.0284
7	0.85	0.0173
Total	5.03	0.7673

Calculations -

t_/2,n-1 = t_0.02/2,7-1 = t_0.01,6 = 3.1427

So,

Confidence interval for population mean is -

Hence, 98% confidence interval of estimate of the mean amount of mercury in the population is (0.2938, 1.1434).

Yes, it appears that there is too much mercury in tuna sushi, because it is possible that 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.

Option A is correct.

Note - t-table is provided below.