# Finding the bias of a random sample

Tags:
1. Mar 8, 2015

### hahaha158

1. The problem statement, all variables and given/known data
In a study to estimate the proportion of residents in a city that support the construction of a new bypass road in the vicinity, a random sample of 2025 residents were polled. Let X denote the number in the sample who supported the proposal. To estimate the true proportion in support of the plan, we can compute p =(X+sqrt(2025)/2)/2025. What is the bias of the estimator p?

2. Relevant equations

3. The attempt at a solution

I am not too sure how to find the bias, can someone tell me what formula I am looking for, or how I should start?

All I could find was on wikipedia that the bias is Expected value(θ' - θ). I am assuming θ' is 2025? How do I continue from here?
Thanks

2. Mar 9, 2015

### Stephen Tashi

The estimator p is a random variable. To see if it is biased, you must find it's expected value and the compare the expected value to the mean of the population. Using "E()" to denote "expected value of", start by writing E(p) = E( ( X + sqrt(2025)/2)/2025 ). You have use facts about the expected values of sums of random variables and the expected value of the product of a constant times a random variables.