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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 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 42% of the respondents said they think their president can control the price of gasoline. 
c) Compare the results from parts (a) and (b).

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(a) What is the minimum sample size needed assuming that no prior information is available?

(b) What is the minimum sample size needed using a prior study that found that 42% of the respondents said they think their president can control the price of gasoline?

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