In a survey to determine the fraction p of supporters of a certain measure in a large population, we take a sample of si
Posted: Tue Nov 23, 2021 9:19 am
In a survey to determine the fraction p of supporters of a
certain measure in a large population, we take a sample of size n.
Suppose we know that 25% of the respondents will lie, and say
exactly the opposite of what they think. It is a large populations,
so we can assume that responses are i.i.d. r.v.’s Xi, each with the
probability of positive answer which is the appropriate function of
p. (I) Suppose k out of n respond that they support the measure,
and find a method of moments estimator for the fraction p of
supporters. (II) Is the estimator found in Part I
unbiased?
certain measure in a large population, we take a sample of size n.
Suppose we know that 25% of the respondents will lie, and say
exactly the opposite of what they think. It is a large populations,
so we can assume that responses are i.i.d. r.v.’s Xi, each with the
probability of positive answer which is the appropriate function of
p. (I) Suppose k out of n respond that they support the measure,
and find a method of moments estimator for the fraction p of
supporters. (II) Is the estimator found in Part I
unbiased?