Question

In a survey, the planning value for the population proportion is p* = 0.26. How large a sample should be taken to provide a 95% confidence interval with a margin of error of 0.05? (Round your answer up to nearest whole number.)

Answer 1

Solution :

Given that,

= 0.26

1 - = 1 - 0.26 = 0.74

margin of error = E = 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 * 0.26 * 0.74

= 295.64

Sample size = 296