Question 4: You are a staff member of a planning agency which wants to gather pu

Question

Question 4: You are a staff member of a planning agency which wants to gather public opinion about a proposal to construct a new nuclear power plant within a 200 mile radius of your urban area. The y has given you $20,000 to canvass area voters on this issue. You have estimated the cost of each administered survey to be $10. The agency wants you to find the proportion of voters in favor of the decision within an accuracy of +/-0.020 and at a confidence level of 95%. Not knowing the true population proportion, you decide to be conservative by assuming a maximum standard error (which sets the population proportion at 0.5) (a) What is the minimum necessary sample size which will provide the desired level of accuracy at a 95% confidence level? (b) Can the survey be conducted within the given budget? Hint: Do you recall the formula for sample size?

Explanation / Answer

a)

b) as amount required to conduct this survey is 2401*10 =24010 which is more than budgert,

therefore this survey can not be conducted in this budget,

here margin of error E = 0.02 for95% CI crtiical Z          = 1.9600 estimated proportion=p= 0.5000 required sample size n =         p*(1-p)*(/E)2= 2401.00

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