Question

A survey study is to be made to estimate the proportion of residents of a certain suburb who favor the construction of a public park near the suburb. The survey will ask at least 30 residents about their opinion regarding the construction. How large a sample is needed if one wishes to be at least 95% confident that the estimate is within 0.04 of the true proportion of residents favoring the construction of the public park?

Answer 1

Answer: 601

Step-by-step explanation:

When the prior estimate of population proportion is not given , the formula we apply to find sample size :

$n=0.25(\dfrac{z^*}{E})^2$

, where z* = critical z-value

E=Margin of error

Given : Margin of error = 0.04

Confidence level = 95%

We know that , according to the z-table , the critical value for 95% confidence interval = z*= 1.960

Then, the required sample size : $n=0.25(\dfrac{1.960}{0.04})^2$

$n=0.25(49)^2$

$n=0.25(2401)=600.25\approx601$

Hence, the required minimum sample size = 601