Question

In a study to estimate the proportion of residents in a city supporting the construction of a new bypass road, a random sample of residents was polled. Let

^
p
^
denote the number in the sample who supported the proposal. To estimate the true proportion in support of the plan, we can compute the estimator
^
p
^​
. The bias of
^
p
^
is:
a) Always zero
b) Always positive
c) Always negative
d) Zero on average, but may not be zero for a specific sample
Choose the correct answer.

Answer 1

The bias of ^p^ is zero on average, but may not be zero for a specific sample. Option d

Step-by-step explanation:

The bias of ^p^ is d) Zero on average, but may not be zero for a specific sample.

In statistics, bias refers to the tendency of an estimator to consistently overestimate or underestimate the true parameter being estimated. In the case of estimating the proportion of residents supporting the construction of a new bypass road, the estimator ^p^ may be unbiased, meaning that on average it provides an accurate estimate of the true proportion.

However, for a specific sample, ^p^ may not be equal to the true proportion, resulting in potential bias. Option d