A researches wishes to estimate, with 95% confidence, the population proportion

Question

A researches 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 avilable. Find the minimum sample size needed. n= ?
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.
n= ?
c) How do the the results from (a) and (b) compare?
A researches 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 avilable. Find the minimum sample size needed. n= ?
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.
n= ?
c) How do the the results from (a) and (b) compare?

a) No preliminary estimate is avilable. Find the minimum sample size needed. n= ?
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.
n= ?
c) How do the the results from (a) and (b) compare?

Explanation / Answer

A)
"no preliminary estimate is available" so assume that p = 0.5

q=1-p

q=1-0.5

q=0.5

n = p(q)(z/E)^2
n = 0.5(0.5)(1.96/0.04)^2

n=0.25(1.96/0.04)^2

n = 600.25

The required sample size is 601

B)
Now we are told that p = 0.28
n = p(1-p)(z/E)^2
n = 0.28(1-0.28)(1.96/0.04)^2
n=0.2016(2401)

n=484.0416
n=485

C)the second minimum sample size smaller than first sample size there is first and second sample size difference will be 116.

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