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

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 1% 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 34% 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) for no  preliminary estimate ; estimated p=0.5

b)

c) requirement of sample size is higher in part a) to compensate for uncertainity in population proportion.

here margin of error E = 0.01 for90% CI crtiical Z          = 1.6449 estimated proportion=p= 0.5000 required sample size n =         p*(1-p)*(/E)2= 6764.00

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