Question

Use the given data to find the minimum sample size required to estimate a population proportion or percentage.

Margin of​ error: five percentage​ points; confidence level 95​%; from a prior​ study, Modifying Above p with caret is estimated by the decimal equivalent of 58​%

Answer 1

Solution :

Given that,

=58% = 0.58

1 - = 1 - 0.58= 0.42

margin of error = E = 5% = 0.05

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96 ( Using z table ( see the 0.025 value in standard normal (z) table corresponding z value is 1.96 )

Sample size = n = (Z_/2 / E)² * * (1 - )

= (1.96 / 0.05)² * 0.58 * 0.42

= 374.32

Sample size = 374