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.) what sample size is necessary if the 95% ci for p is to have a width of at most 0.18 irrespective of p?

Answer 1

To determine the necessary sample size, we can use the formula n = (Z^2 * p * (1 - p)) / E^2, where Z is the z-score corresponding to the desired confidence level, p is the estimated proportion, and E is the maximum allowable margin of error. Plugging in the values, we find that the necessary sample size is 89.

Step-by-step explanation:

To determine the necessary sample size, we need to use the formula:

n = (Z^2 * p * (1 - p)) / E^2

Where:

Z is the z-score corresponding to the desired confidence level (95% = 1.96),

p is the estimated proportion (unknown, so we assume p = 0.5 for maximum sample size),

E is the maximum allowable margin of error (0.18).

Plugging in the values, we get:

n = (1.96^2 * 0.5 * (1 - 0.5)) / 0.18^2

n ≈ 2.86 / 0.0324

n ≈ 88.27

Rounding up to the nearest integer, the required sample size is 89.