Question

A state legislator wishes to survey residents of her district to see what proportion of the electorate is aware of her position on using state funds to pay for abortions. (Round your answers up to the nearest integer.)

(a)

What sample size is necessary if the 95% CI for p is to have a width of at most 0.16 irrespective of p?

(b)

If the legislator has strong reason to believe that at least

7

8

of the electorate know of her position, how large a sample size would you recommend to maintain a width of at most 0.16?

Answer 1

a)

The following information is provided,
Significance Level, α = 0.05, Margin of Error, E = 0.08

The provided estimate of proportion p is, p = 0.5
The critical value for significance level, α = 0.05 is 1.96.

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)*(1.96/0.08)^2
n = 150.06

Therefore, the sample size needed to satisfy the condition n >= 150.06 and it must be an integer number, we conclude that the minimum required sample size is n = 151
Ans : Sample size, n = 151 or 150

b)

The following information is provided,
Significance Level, α = 0.05, Margin of Error, E = 0.08

The provided estimate of proportion p is, p = 0.875
The critical value for significance level, α = 0.05 is 1.96.

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 = 0.875*(1 - 0.875)*(1.96/0.08)^2
n = 65.65

Therefore, the sample size needed to satisfy the condition n >= 65.65 and it must be an integer number, we conclude that the minimum required sample size is n = 66
Ans : Sample size, n = 66 or 65