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 5% 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) (a) What is the minimum sample size needed assuming that no prior information is available? nRound up to the nearest whole number as needed.) b) What is 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? n= | | (Round up to the nearest whole number as needed.) (c) How do the results from (a) and (b) compare? 0 A. Having an estimate of the population proportion has no effect on the minimum sample size needed 0 B. Having an estimate of the population proportion reduces the minimum sample size needed. ° C. Having an estimate of the population proportion raises the minimum sample size needed.

Explanation / Answer

a) for no prior information p=0.5

margin of error E =0.05

and for 95% CI ; critical z =1.96

therefore sample size requried n =p(1-p)*(Z/E)2 =385

b) for p=0.34

sample size requried n =p(1-p)*(Z/E)2 = 345

c)

option B is correct

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