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?
0.58 0.80 0.09 0.95 1.32
What is the confidence interval estimate of the population mean μ?
_____ppm<μ<_____ppm (Round to 3 Decimal places as needed)
Does it appear that there is too much mercury in tuna sushi?
For the data given, we have the following descriptive statistics calculated using a statistics tool:
Sample size, n = 7
Sample mean, m = 0.76
Sample standard deviation, S = 0.388
Degrees of freedom, df = n-1 = 6
Standard error of mean, SE = S/(n^0.5) = 0.388/(6^0.5) = 0.158
For a 98% confidence interval, the critical t-value with df = 6 is:
tc = 3.14
So, the 98% CI is as follows:
m - (tc*SE) < μ < m + (tc*SE)
Put the respective values:
0.76 - (3.14*0.158) < μ < 0.76 + (3.14*0.158)
0.263 < μ < 1.256
Since this interval also contains the values above 1, so we can say that it appears that there is too much mercury in tuna sushi.
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