Question

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

Answer 1

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.