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Ch. 7 - Estimating Parameters and Determining Sample Sizes
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 7 - Estimating Parameters and Determining Sample SizesProblem 7.2.19
Chapter 7, Problem 7.2.19

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

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Step 1: Identify the given data and the requirements of the problem. The data provided are the mercury levels in ppm: 0.56, 0.75, 0.10, 0.95, 1.25, 0.54, and 0.88. The task is to construct a 98% confidence interval for the mean mercury level in the population and determine if the mean exceeds the FDA guideline of 1 ppm.
Step 2: Calculate the sample mean (\( \bar{x} \)) and the sample standard deviation (\( s \)). Use the formulas \( \bar{x} = \frac{\sum x_i}{n} \) for the mean and \( s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}} \) for the standard deviation, where \( n \) is the sample size and \( x_i \) are the individual data points.
Step 3: Determine the critical value for a 98% confidence level. Since the sample size is small (n = 7) and the population standard deviation is unknown, use the t-distribution. Find the t-value corresponding to a 98% confidence level and degrees of freedom \( df = n - 1 \).
Step 4: Calculate the margin of error (ME) using the formula \( ME = t \cdot \frac{s}{\sqrt{n}} \), where \( t \) is the critical value, \( s \) is the sample standard deviation, and \( n \) is the sample size.
Step 5: Construct the confidence interval using the formula \( \text{Confidence Interval} = \bar{x} \pm ME \). Interpret the interval to determine if the mean mercury level in the population exceeds the FDA guideline of 1 ppm.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Confidence Interval

A confidence interval is a range of values, derived from sample statistics, that is likely to contain the true population parameter with a specified level of confidence, such as 98%. It provides an estimate of uncertainty around the sample mean, allowing researchers to infer about the population mean. The wider the interval, the more uncertainty there is about the estimate.
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Mean and Standard Deviation

The mean is the average of a set of values, calculated by summing all values and dividing by the number of observations. The standard deviation measures the dispersion of the data points around the mean, indicating how spread out the values are. Together, these statistics are essential for constructing confidence intervals and understanding the data's variability.
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Hypothesis Testing

Hypothesis testing is a statistical method used to determine whether there is enough evidence in a sample to support a specific claim about a population parameter. In this context, it involves testing whether the mean mercury level in tuna sushi exceeds the FDA guideline of 1 ppm. The results can help assess the safety of consuming tuna sushi based on the sample data.
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Step 1: Write Hypotheses
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