Question

An educator wants to estimate the proportion of school children in Boston who are living with only one parent. However, their funding is limited so they do not want to collect a larger sample than necessary. They hope to use a sample size such that, with probability 0.95, the error will not exceed 0.025. What sample size will ensure this, regardless of what sample proportion value occurs when they gather the sample (no preliminary estimate for p)?

A. The critical value, z_c=  (round to 2 decimal places).

B. The sample size, n =  .

Answer 1

Solution :

Given that,

= 0.5 ( assume 0.5)

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.025

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

Zc=1.96

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

= (1.96 / 0.025)2 * 0.5 * 0.5

= 1536.64

Sample size =1537