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

Answer:

The number of judges that should be selected  is 25

Step-by-step 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:

$E = Z_{\alpha/2} \times \dfrac{s}{\sqrt{n}}$

$2 = 1.645 \times \dfrac{6.11}{\sqrt{n}}$

$2\sqrt{n} = 10.05095$

$\sqrt{n} = \dfrac{10.05095}{2}$

$\sqrt{n} =5.026$

$n=(5.026)^2$

n = 25.26

n ≅ 25