A researcher wishes to estimate, with 95 % confidence, the population proportion

Question

A researcher wishes to estimate, with 95 % confidence, the population proportion of adults who think the president of their country can control the price of gasoline. Her estimate must be accurate within 3 % of the true proportion. a) No preliminary estimate is available. Find the minimum sample size needed.b) Find the minimum sample size needed, using a prior study that found that 28 % of the respondents said they think their president can control the price of gasoline. c) Compare the results from parts (a) and (b).

(a) What is the minimum sample size needed assuming that no prior information is available? [] (Round up to the nearest whole number as needed.)

(b) What is the minimum sample size needed using a prior study that found that 28 % of the respondents said they think their president can control the price of gasoline? [] (Round up to the nearest whole number as needed.)

(c) How do the results from (a) and (b) compare?

Explanation / Answer

a) Use p=0.5 when no prior estimate is available. So the calculation is as mentioned below:-

n=Za/2^2*p*(1-p)/e^2=(1.96)^2*0.5*0.5/(0.03)^2=1067.11 and so it would be 1068

b) n=Za/2^2*p*(1-p)/e^2=(1.96)^2*0.28*0.72/(0.03)^2=860.5184=861

c) When the proportion of success is less, the sample number is also less.

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