19 - When we choose many SRSs from a population, the...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
When we choose many SRSs from a population, the sampling distribution of the sample means is centered at the mean of the original population and is less spread out than the distribution of individual observations. Here are the facts. Suppose that is the mean of an SRS of size n drawn from a large population with mean μ and standard deviation σ. Then the sampling distribution of has mean μ and standard deviation σ/√ n . # The mean of the statistic is always equal to the mean μ of the population. That is, the sampling distribution of is centered at μ. In repeated sampling, will sometimes fall above the true value of the parameter μ and sometimes below, but there is no systematic tendency to overestimate or underestimate the parameter. This makes the idea of lack of bias in the sense of “no favoritism” more precise. Because the mean of is equal to μ, we say that the statistic is an unbiased estimator of the parameter μ. # An unbiased estimator is “correct on the average” in many samples. How close the estimator falls to the parameter in most samples is determined by the spread of the sampling distribution. If
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/27/2012 for the course STAT 121 taught by Professor Patticolling during the Winter '11 term at BYU.

Page1 / 2

19 - When we choose many SRSs from a population, the...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online