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

See Explanation

Step-by-step explanation:

Given

`N = 1975` --- Population

`s = 142` --- Selected

Required

Determine the sample size (n) using:
`n = (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 = (s)/(N)`

`p = (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 = (z^2\sigma^2)/(E^2)` becomes

`n = (z^2 * 131.79)/(E^2)`

Assumptions:

`z = 1.96`

`E = 10`

`n = (1.96^2 * 131.79)/(10^2)`

`n = (3.8416 * 131.79)/(100)`

`n = 5.06`

Round up:
`n = 6`