Question

A population has a standard deviation x=18.4. How large a sample must be drawn so that a 98% confidence interval will have a margin of error equal to 4.1?

Answer 1

"109" will be the appropriate response.

Explanation:

The given values are:

Standard deviation,

`\sigma=18.4`

Margin of error,

`E = 4.1`

Using the table,

`Z_{((0.02)/(2) )}=2.326`

Now,

The sample size will be:

⇒
`n=(\frac{Z_{((0.02)/(2))* \sigma}}{E} )^2`

On substituting the values, we get

⇒
`=((2.326* 18.4)/(4.1) )^2`

⇒
`=((42.7984)/(4.1) )^2`

⇒
`=(10.4386341)^2`

⇒
`=109`