Question

The 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 0.23. 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 0.037 Round your answer up to the next integer. Answer/How to Enter) 2 Points Tables Keypad Keyboard Shortcuts Hawkes Learning

Answer 1

Solution:

Given,

E = 0.03

c = 95% = 0.95

p = 0.23

1- p = 1 - 0.23 = 0.77

Now,

$url=https://latex.codecogs.com/gif.latex?%5Calpha&t=1596240407&ymreqid=f4764063-0d40-e2b0-1cde-f00281012f00&sig=K6NQgcpTjaZFX_nx89zTZg--~D$ = 1 - c = 1 - 0.95 = 0.05

$url=https://latex.codecogs.com/gif.latex?%5Calpha&t=1596240407&ymreqid=f4764063-0d40-e2b0-1cde-f00281012f00&sig=K6NQgcpTjaZFX_nx89zTZg--~D$/2 = 0.025

$url=https://latex.codecogs.com/gif.latex?%5Ctherefore&t=1596240407&ymreqid=f4764063-0d40-e2b0-1cde-f00281012f00&sig=64JCe_IJZ7qxztE0mA_rRg--~D$$url=https://latex.codecogs.com/gif.latex?z_%7B%5Calpha/2%7D&t=1596240407&ymreqid=f4764063-0d40-e2b0-1cde-f00281012f00&sig=nLa9lzRtdgLfe1QOpoG.ZQ--~D$ = 1.96 (using z table)

The sample size for estimating the proportion is given by

n =

/2P(1 - p) E2

= (1.96)² * 0.23 * 0.77 / (0.03²)

= 755.94

= 756 ..(round to the next whole number)

Answer is

756