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

0.60   0.71 0.10 0.96 1.34 0.54 0.92

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

Answer 1

Step 1:

Ho: ≥ 1

Ha: < 1

Step 2: Test statistics

n = 7

sample mean = 5.17 / 7 = 0.7386

sample sd = s

data	data-mean	(data - mean)2
0.60	-0.1386	0.01920996
0.71	-0.0286	0.00081796
0.10	-0.6386	0.40780996
0.96	0.2214	0.04901796
1.34	0.6014	0.36168196
0.54	-0.1986	0.03944196
0.92	0.1814	0.03290596

s = 0.3896

Assuming that the data is normally distributed and also as the population sd is not given, we will use t stat.

t = -1.775

Step 3:

Assuming =0.05

t critical for left tailed test = - 1.9432

As t stat does not fall in the rejection area, we fail to reject the Null hypothesis.

Confidence interval

t value for CI = TINV(0.05, 6) = 2.447

CI = mean +/- E = 0.7386 +/- 0.360

CI = 0.378 , 1.099

As 1 is in the CI range, we fail to reject the Null hypothesis.