PLEASE HELP WILL MARK BRAINLIEST AND GIVE 50 POINTS
The manufacturer wants to estimate the percent of television viewers who watch a program. The manufacturer wants the estimate to have a margin of error of at most 0.02 at a level of 95 percent confidence. Of the following, which is the smallest sample size that will satisfy the manufacturer’s requirements?
a. 40
b. 50
c. 100
d. 1700
e. 2500
I just need to understand why the answer is e. 2500; thanks!

Respuesta :

Answer:

The correct option is;

e. 2500

Step-by-step explanation:

The formula for sample size is given by the following formula;

[tex]n = \dfrac{z^2 \times \hat p(1 - \hat p)}{\epsilon ^2}[/tex]

At 95%, z = 1.96

ε = Margin of error = 0.02 = 2%

Finding the sample size, n, given only the margin of error is by the following formula;

Margin of error = 100/√n

Therefore, we have;

2 = 100/√n

√n = 100/2 = 50

n = 50² = 2500

Therefore, the correct option is e. 2500.

Answer:

The correct option is;

e. 2500

Step-by-step explanation: