Question

How many judges should be selected to estimate the population mean wage with 90% confidence and a margin of error of $2.00

Answer 1

The number of judges that should be selected is 25

Explanation:

Given that:

The C.I = 90%

Level of significance = 1 - C.I

= 1 - 0.90

= 0.10

Critical level for
`Z_(\alpha/2)` at 0.10 = 1.645

The margin of error E = 2.00

Let's assume that the sample standard deviation was $6.11

Then;

The number of judges that should be selected can be computed by using the formula:

`E = Z_(\alpha/2) * (s)/(√(n))`

`2 = 1.645 * (6.11)/(√(n))`

`2√(n) = 10.05095`

`√(n) = (10.05095)/(2)`

`√(n) =5.026`

`n=(5.026)^2`

n = 25.26

n ≅ 25