Question

If the estimate of expected population proportion having a desired characteristic based on intuition is 60 percent and the acceptable error is plus or minus 5 percent, and the z-value for a 95 percent level of confidence is 1.96, the needed sample size is approximately:

A. 187
B. 368
C. 295
D. 196
E. 950

Answer 1

B

Explanation:

Our values are:

N = 100,000 (We assume it)

Proportion is p = 0.6

Margin of error (E) = 0.05

confidence-level (cl) = 0.95

Z-value = 1.96

We need to approach through Proportion,

`n=( (z_2 * p *q) + ME_2)/(ME_2 + z_2 * p * q / N)`

Substituting,

`n = ((1.962*0.6*0.4)+0.052)/(0.052 + (1.962 * 0.6 * 0.4)/(100000))`

`n= ((3.841 * 0.24)+0.0025)/(0.0025+(3.841*0.24)/(100000))`

`n =( 0.9243)/(0.002509)`

`n= 368`