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?

Accepted Solution

Answer: 601Step-by-step explanation:When the prior estimate of population proportion is not given , the formula we apply to find sample size :[tex]n=0.25(\dfrac{z^*}{E})^2[/tex], where z* = critical z-value E=Margin of errorGiven : Margin of error = 0.04Confidence level = 95%We know that , according to the z-table , the critical value for 95% confidence interval = z*= 1.960Then, the required sample size : [tex]n=0.25(\dfrac{1.960}{0.04})^2[/tex] [tex]n=0.25(49)^2[/tex] [tex]n=0.25(2401)=600.25\approx601[/tex]Hence, the required minimum sample size = 601