Question

7. What is the minimum sample size needed to ensure a survey to create a confidence interval estimate of a population proportion has a margin of error no larger than 0.09 at the 98% confidence level?

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E =0.09

At 98% confidence level the z is,

= 1 - 98%

= 1 - 0.98 = 0.02

/2 = 0.01

Z/2 = 2.326 ( Using z table )

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

= (2.326 / 0.09)2 * 0.5 * 0.5

=166.98

Sample size = 167 (rounded accurate )

167 minimum sample size needed to ensure a survey