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

Answer:

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.

Step-by-step explanation:

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

$\alpha = \frac{1-0.95}{2} = 0.025$

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

$E = z*\frac{\sigma}{\sqrt{n}}$

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

$E = 1.96\frac{8}{\sqrt{110}} = 1.495$

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.