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Answer:
The confidence interval estimate of the population mean is :
(0.61 ppm, 0.90 ppm)
The correct option is (A).
Step-by-step explanation:
The amounts of mercury (ppm) found in tuna sushi sampled at different stores in a major city are:
S = {0.58, 0.82, 0.10, 0.98, 1.27, 0.56, 0.96}
A confidence interval for the population mean (μ) is an interval estimate of the true value of the mean. This interval has a
probability of consisting the true value of mean.
⇒ Since the population standard deviation is not provided we will use the <em>t</em>-distribution to construct the 99% confidence interval for mean.
⇒ The formula for confidence interval for the population mean is:
Here,
= sample mean
<em>s </em>= sample standard deviation
<em>n</em> = sample size
= critical value.
The degrees of freedom for the critical value is, (<em>n</em> - 1) = 7 - 1 = 6.
The significance level is:
The critical value is:
**Use the <em>t</em>-table for the critical value.
Compute the sample mean and sample standard deviation as follows:
The 99% confidence interval for μ is:
The confidence interval estimate of the population mean is:
(0.61 ppm, 0.90 ppm)
The upper and lower limit of the 99% confidence interval indicates that the true mean value is less than 1 ppm. This implies that there is not too much mercury in tuna sushi
Because it is possible that the mean is not greater than 1 ppm. Also, at least one of the sample values is less than 1 ppm, so at least some of the fish are safe.
Thus, the correct option is (A).
