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

Answer:

B

Step-by-step 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,

$n=\frac{ (z_2 * p *q) + ME_2}{ME_2 + z_2 * p * q / N}$

Substituting,

$n = \frac{(1.962*0.6*0.4)+0.052}{0.052 + \frac{1.962 * 0.6 * 0.4}{100000}}$

$n= \frac{(3.841 * 0.24)+0.0025}{0.0025+\frac{3.841*0.24}{100000}}$

$n =\frac{ 0.9243}{0.002509}$

$n= 368$