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ozzi
3 years ago
10

A cheese processing company wants to estimate the mean cholesterol content of all one-ounce servings of a type of cheese. The es

timate must be within 0.75 milligrams of the population mean. Determine the minimum sample size required to construct a 95% confidence interval for the population mean. Assume the population standard deviation is 3.10 milligrams
Mathematics
1 answer:
Mrrafil [7]3 years ago
5 0

Answer:

The minimum sample size required to construct a 95% confidence interval for the population mean is 65.

Step-by-step explanation:

We are given the following in the question:

Population standard deviation,

\sigma = 3.10\text{ milligrams}

We need to construct a 95% confidence interval such that the estimate is within 0.75 milligrams of the population mean.

Thus, the margin of error must me 0.75

Formula for margin of error:

z_{critical}\times \dfrac{\sigma}{\sqrt{n}}

z_{critical}\text{ at}~\alpha_{0.05} = 1.96

Putting values, we get,

0.75 = 1.86\times \dfrac{3.10}{\sqrt{n}}\\\\\sqrt{n} = \dfrac{1.96\times 3.10}{0.75}\\\\\sqrt{n} = 8.101\\\Rightarrow n = 65.63\approx 65

Thus, the minimum sample size required to construct a 95% confidence interval for the population mean is 65.

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