The closest to the minimum number of consumers needed to obtain the estimate with the desired precision is (b) 271
Explanation:
When the prior estimate of population proportion is not given , then the formula to find the sample size is given by :-
where E = Margin of error.
z* = Critical z-value.
As per given , we have
E = 5%=0.05
Confidence level = 90%
The critical value of z at 90% is 1.645 (By z-table)
Put all values in the formula , we get
n=0.25(1.645/0.05)²
n=0.25(32.9)²
n=270.6025≈271
Thus, the minimum sample size needed = 271
Hence , the correct answer is 271 .