Question

Determine the sample size the research respondents. taht selected 142 out of 1975 ,a mathematical formula for the purpose of determining the sample size. n =z²σ² E²

Answer 1

Answer:

See Explanation

Explanation:

Given

$N = 1975$ --- Population

$s = 142$ --- Selected

Required

Determine the sample size (n) using: $n = \frac{z^2\sigma^2}{E^2}$

This question is incomplete as the margin of error (E) and the z-score are not given.

To solve this question, I'll assume values for z and E.

Calculating $\sigma^2$

This is calculated as:

$\sigma^2 = N * p * (1 - p)$

Where

$p = \frac{s}{N}$

$p = \frac{142}{1975}$

$p = 0.0719$

So, we have:

$\sigma^2 = N * p * (1 - p)$

$\sigma^2 = 1975 * 0.0719 * (1 - 0.0719)$

$\sigma^2 = 131.79$

The formula: $n = \frac{z^2\sigma^2}{E^2}$ becomes

$n = \frac{z^2 * 131.79}{E^2}$

Assumptions:

$z = 1.96$

$E = 10$

$n = \frac{1.96^2 * 131.79}{10^2}$

$n = \frac{3.8416 * 131.79}{100}$

$n = 5.06$

Round up: $n = 6$