Mercury in Sushi An FDA guideline is that the mercury in fish ...

Question

Mercury in Sushi An FDA 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 New York City. The study was sponsored by the New York Times, and the stores (in order) are D’Agostino, Eli’s Manhattan, Fairway, Food Emporium, Gourmet Garage, Grace’s Marketplace, and Whole Foods. 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?

0.56 0.75 0.10 0.95 1.25 0.54 0.88

0.56 0.75 0.10 0.95 1.25 0.54 0.88

Accepted Answer

Hello everyone. Let's take a look at this question together. A study measures the arsenic concentration in parts per million in rice samples from seven different brands. 0.21, 0.32, 0.18, 0.29, 0.24, 0.27, and 0.31. The FDA recommends that arsenic levels should not exceed 0.30 parts per million. Construct a 98% confidence interval for the mean arsenic concentration in these rice samples. Does the interval suggest that the mean arsenic level may be too high? So in order to solve this question, we have To recall how to construct a 98% confidence interval for the mean arsenic concentration in these rice samples, and if the interval suggests that the mean arsenic level may be too high. So from the information in the question, we have our arsenic concentrations in parts per million. Which is our data set. As well as our sample size, which is represented as N, is equal to 7, and we also need our sample mean, which is X bar, which is calculated by the sum of our sample data divided by the sample size. Which is equal to 0.26. And we also need our sample standard deviation, which is represented as S. And can be calculated using the formula for the sample standard deviation. Which using the values from this table, we can substitute them into the sample standard deviation formula and get our sample standard deviation value of 0.048. And then we can find our T critical value for the 98% confidence interval. Where we have our degrees of freedom equaling and minus 1, so it is equal to 6, and for a 98% confidence interval with a degree of freedom equaling 6, the T distribution critical value which we obtain from a T table or a calculator is equal to 3.143, and then we can calculate. Our margin of error, which can be calculated using the formula for the margin of error, which is our criticalt value multiplied by our sample standard deviation divided by the square root of our sample size, and plugging in our values for the margin of error formula, we get 0.0570 as the value for our margin of error. And using this value, we can then calculate our confidence interval. By using the formula for the confidence interval, which is equal to X bar, our sample mean, plus or minus our margin of error. And plugging in the values into the formula, our confidence interval is 0.203 to 0.317. So our 98% confidence interval for the arsenic concentration in parts per million in the rice samples from the seven different brands is 0.203 to 0.317 parts per million, and we know that the FDA limit is 0.30 parts per million. Well, since 0.30 is within the interval, there is a possibility that the mean arsenic concentration could be at or above the recommended limit. Therefore, the correct answer choice is answer choice B, as it contains the correct confidence interval values, and the mean may be too high, since the upper limit of the interval exceeds the FDA recommendation. And all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

Key Concepts

Confidence Interval

Mean and Standard Deviation

Hypothesis Testing

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