Question

How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 95% confidence level with an error of at most 0.02

Answer 1

Complete question:

A state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. In an earlier study, the population proportion was estimated to be 0.18.

How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 95% confidence level with an error of at most 0.02? Round your answer up to the next integer.

Answer:

1418

Step-by-step explanation:

Given:

Sample proportion = 0.18

Level of significance = 1 - 0.95 = 0.05

u.E = 0.02

Required:

Find the sample size.

To find the sample size, n, use tge formula:

$n = \frac{(Z_a_/_2)^2 p(1 - p)}{u.E^2}$

Using the Z table, $Z_0_._0_5_/_2$ = 1.96

Thus,

$n = \frac{1.96^2 * 0.18(1 - 0.18)}{0.02^2}$

$n = 3.8451 * 0.1476}{0.0004}$

$n = 1417.55$

Approximately 1418

Sample size woulb be 1418