Question

A laboratory tested n = 110 chicken eggs and found that the mean amount of cholesterol was LaTeX: \bar{x}x ¯ = 92 milligrams with σ = 8 milligrams. Find the margin of error E corresponding to a 95% confidence interval for the true mean cholesterol content, μ, of all such eggs.

Answer 1

The margin of error corresponding to a 95% confidence interval for the true mean cholesterol content, μ, of all such eggs is of 1.495 miligrams.

Explanation:

We have that to find our
`\alpha` level, that is the subtraction of 1 by the confidence interval divided by 2. So:

`\alpha = (1-0.95)/(2) = 0.025`

Now, we have to find z in the Ztable as such z has a pvalue of
`1-\alpha`.

So it is z with a pvalue of
`1-0.025 = 0.975`, so
`z = 1.96`

Now, find the margin of error E as such

`E = z*(\sigma)/(√(n))`

In which
`\sigma` is the standard deviation of the population and n is the size of the sample.

In this question:

`\sigma = 8, n = 110`. So

`E = 1.96(8)/(√(110)) = 1.495`

The margin of error corresponding to a 95% confidence interval for the true mean cholesterol content, μ, of all such eggs is of 1.495 miligrams.