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 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 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 that no prior information is available? (b) What is the minimum sample size needed using a prior study that found that 26% of the respondents said they think their president can control the price of gasoline? (c) How do the results from (a) and (b) compare? A. Having an estimate of the population proportion reduces the minimum sample size needed B. Having an estimate of the population proportion raises the minimum sample size needed C. Having an estimate of the population proportion needed has no effect on the minimum sample size needed

Explanation / Answer

e = 0.05 , for 90 % confidence , z= 1.645

estimate of p is not known

so n = z^2/(4e^2)

= (1.645^2 / (4*0.05^2))

=270.6025

n = 271

b) when estiamte of p is known

n =z^2*pq/e^2

= 1.645^2 *0.28*0.72/0.05^2

=218.213856

n = 219

c) since 219 < 271

have population estiamte reduces the sample size

option A) is correct

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