A researcher wants to make a 99% confidence interval for the population proportion. The most conservative estimate of the sample size that would limit the maximum error of estimate to within. 05 of the population proportion is at least:

(A) 1274

(B) 666

(C) 26

(D) 1128

(B) sample size is 666

Step-by-step explanation:

given data

CI = 99%

error = 0.05

to find out

sample size

solution

we know that for CI = 99% and E = 0.05 the value of z = 2.58 from table

and no estimate of proportion is given so it is rule take q = p = 0.5

so now we can calculate sample size i. e.

n = (z/E) ² * p * q

put the value q and p = 0.5 and z and E so we get sample size

n = (z/E) ² * p * q

n = (2.58/0.05) ² * 0.5 * 0.5

n = 665.64

so sample size is 666

so option (B) is right