Question

A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within

3 percentage points with 99% confidence if

​(a) he uses a previous estimate of

25%?

​(b) he does not use any prior​ estimates?

Answer 1

a)

The following information is provided,
Significance Level, α = 0.01, Margin of Error, E = 0.03

The provided estimate of proportion p is, p = 0.25
The critical value for significance level, α = 0.01 is 2.58.

The following formula is used to compute the minimum sample size required to estimate the population proportion p within the required margin of error:
n >= p*(1-p)*(zc/E)^2
n = 0.25*(1 - 0.25)*(2.58/0.03)^2
n = 1386.75

Therefore, the sample size needed to satisfy the condition n >= 1386.75 and it must be an integer number, we conclude that the minimum required sample size is n = 1387
Ans : Sample size, n = 1387

b)

The following information is provided,
Significance Level, α = 0.01, Margin of Error, E = 0.03

The provided estimate of proportion p is, p = 0.5
The critical value for significance level, α = 0.01 is 2.58.

The following formula is used to compute the minimum sample size required to estimate the population proportion p within the required margin of error:
n >= p*(1-p)*(zc/E)^2
n = 0.5*(1 - 0.5)*(2.58/0.03)^2
n = 1849

Therefore, the sample size needed to satisfy the condition n >= 1849 and it must be an integer number, we conclude that the minimum required sample size is n = 1849
Ans : Sample size, n = 1849

## iF you take z value upto 3 deciaml i.e. 2.576 answer would be change