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

The margin of error is of 1.5 milligrams.

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 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(\sigma)/(√(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(\sigma)/(√(n))`

`M = 1.96(9)/(√(130))`

`M = 1.5`

The margin of error is of 1.5 milligrams.