A state legislator wishes to survey residents of her district to see what propor

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 0.17 irrespective of p? 161 X people (b) If the legislator has strong reason to believe that at leastof the electorate know of her position, how large a sample size would you recommend to maintain a width of at most 0.17? people

Explanation / Answer

this is a margion of error question

b Z0.05/2*(p*(1-p)/n)1/2 = 0.17 where p =0.66

Z0.025*(0.2244/n)1/2 = 0.17 => 1.96*(0.2244/n)1/2 = 0.17

a

        Z0.05/2*(p*(1-p)/n)1/2 = 0.17 => 1.96*(p*(1-p)/n)1/2 = 0.17

while for p*(1-p), when p=1/2, p*(1-p) arrive maximum and maximum value is ¼, so n =140*1/4 =35

So if no estimate were available for the proportion so n= 35

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