Question

A laboratory tested n= 130 chicken eggs and found that the mean amount of cholesterol was 88 milligrams with -9 milligrams. Find the margin of error E corresponding to a 95% confidence interval for the true mean cholesterol content of all such eggs. Round your answer to the nearest tenth.

Answer 1

Answer:

The margin of error is of 1.5 milligrams.

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 Z-table as such z has a p-value of $1 - \alpha$.

That is z with a pvalue of $1 - 0.025 = 0.975$, so Z = 1.96.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

Standard deviation of 9

This means that $\sigma = 9$

Sample of 130

This means that $n = 130$

Find the margin of error E corresponding to a 95% confidence interval for the true mean cholesterol content of all such eggs.

$M = z\frac{\sigma}{\sqrt{n}}$

$M = 1.96\frac{9}{\sqrt{130}}$

$M = 1.5$

The margin of error is of 1.5 milligrams.