Bias and Unbiased Estimators for Sampling Distributions

A statistic used to estimate a parameter is an ____________ if the mean of its sampling distribution is equal to the value of the parameter being estimated.

• unbiased estiamtor

• biased estimator

• highly variable

• less variable

Which best describes the sampling distribution shown below.

• Unbiased Estimator

• Biased Estimator

Which best describes the sampling distribution shown below.

• Unbiased Estimator

• Biased Estimator

A statistic is an unbiased estimator of a parameter when

• in many samples, the values of the statistic are centered at the parameter

• in many samples, the values of the statistic are close to the parameter

• the statistic is calculated from a random sample.

• in a single sample, the value of the statistic is equal to the parameter

True or False: A statistic used to estimate a parameter is an unbiased estimator if the mean of its sampling distribution is equal to the value of the parameter being estimated.

• True

• False

When the mean of a sampling distribution is the same as that of the population, we say that

• it is an unbiased estimator of the population

• it is an unbiased estimator of the statistic

• it is a low variability estimator of the population

• it is a biased estimator of the population

Researchers will conduct a study of the television-viewing habits of children. They will select a simple random sample of children and record the number of hours of television the children watch per week. The researchers will report the sample mean as a point estimate for the population mean. Which of the following statements is correct for the sample mean as a point estimator?

• A sample of size 25 will produce more variability of the estimator than a sample of size 50.

• A sample of size 25 will produce less variability of the estimator than a sample of size 50.

• A sample of size 25 will produce a biased estimator, but a sample size of 50 will produce an unbiased estimator.

• A sample of size 25 will produce a more biased estimator than a sample of size 50.

• A sample of size 25 will produce a less biased estimator than a sample of size 50.

The following graphs show the sampling distributions for two different point estimators, R and W, of the same population parameter. Which of the following statements is true?

• Both R and W are unbiased.

• R is biased, and W is unbiased

• Both R and W are biased.

• R is unbiased, and W is biased.

• The assessment of bias is not possible, because the sampling distributions display too much variability.

A statistic is biased if...

• the value of the statistic from any sample is NOT equal to the parameter

• The value of the statistic from any sample IS equal to the parameter

• The mean of the sampling distribution is NOT equal to the true value of the parameter

• The mean of the sampling distribution IS equal to the value of the parameter