Construct the confidence interval estimate of the mean. An...

Construct the confidence interval estimate of the mean. 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? $$\begin{array}{rrrrrrr} 0.56 & 0.75 & 0.10 & 0.95 & 1.25 & 0.54 & 0.88 \end{array}$$

Construct the confidence interval estimate of the mean.
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?
$$\begin{array}{rrrrrrr}
0.56 & 0.75 & 0.10 & 0.95 & 1.25 & 0.54 & 0.88
\end{array}$$

Key Concepts

Margin of Error

The margin of error represents the extent of the maximum expected difference between the population parameter and the sample estimate. It is calculated by multiplying the critical value from the t-distribution by the standard error, and it determines the width of the confidence interval.

Confidence Level

The confidence level, expressed as a percentage (such as 98%), indicates the degree of certainty that the computed confidence interval contains the true population mean. In practical terms, it means that if the study were repeated many times, a specified proportion of the intervals would include the actual mean.

Sample Standard Deviation

The sample standard deviation is a measure of the spread or variability of the sample data. It quantifies how much the individual observations deviate from the sample mean and is essential for assessing the uncertainty in the estimation process.

Sample Mean

The sample mean is the arithmetic average of the observations in the sample and serves as a point estimate for the population mean. It is computed by summing all sample values and dividing by the number of observations, providing a central value around which the data tend to cluster.

t-distribution

When the sample size is small and the population standard deviation is unknown, the t-distribution is used instead of the normal distribution. This distribution accounts for the additional uncertainty introduced by estimating the standard deviation from the sample, and its shape varies with the degrees of freedom.

Confidence Interval

A confidence interval is a range derived from sample data that is likely to contain the population parameter (in this case, the mean) with a specified level of confidence. It offers a way to express the uncertainty or precision associated with the estimate of the population mean.

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