Question

The ages of registered voters in Smith County are normally distributed with a population standard deviation of 3 years and an unknown population mean. A random sample of 18 voters is taken and results in a sample mean of 55 years. Find the margin of error for a 95% confidence interval for the population mean. 20.01 20.10 1.282 20.05 1.645 20.025 1.960 20.005 2.576 2.326 You may use a calculator or the common z values above. • Round the final answer to two decimal places.

Answer 1

The margin of of error for a 95% confidence interval for the population mean is of 1.39 years.

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`.

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

The margin of error is:

`M = z(\sigma)/(√(n))`

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

Population standard deviation of 3 years

This means that
`\sigma = 3`

Sample of 18 voters

This means that
`n = 18`

Margin of error:

`M = z(\sigma)/(√(n))`

`M = 1.96(3)/(√(18))`

`M = 1.39`

The margin of of error for a 95% confidence interval for the population mean is of 1.39 years.