A researcher wishes to? estimate, with 90?% ?confidence, the population proporti

Question

A researcher wishes to? estimate, with 90?% ?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 4?% 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).

Explanation / Answer

a)

b)

c)

sample size requirement decreases if  prior estimate is known

here margin of error E = 0.04 for90% CI crtiical Z          = 1.645 estimated proportion=p= 0.500 required sample size n =         p*(1-p)*(z/E)2= 423.00

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