Question

What does it mean if a statistic is unbiased?

a. The mean of its sampling distribution is equal to the true value of the parameter being estimated.
b. The sample size is really large.
c. The survey used to obtain the statistic was designed so as to avoid even a hint of racial or sexual prejudice.
d. It is used for only honest purposes.
e. Both the person who calculated the statistic and the subjects whose responses make up the statistic were truthful.

Answer 1

An unbiased statistic means the mean of its sampling distribution is equal to the true population parameter it is intended to estimate, which is accurately described in option (a). Other options referring to sample size, survey design ethics, and truthfulness are unrelated to the statistical definition of 'unbiased'.

Step-by-step explanation:

What It Means for a Statistic to Be Unbiased

An unbiased statistic means that the mean of its sampling distribution is equal to the true value of the parameter being estimated. So, for a statistic to be unbiased, option (a) stating 'The mean of its sampling distribution is equal to the true value of the parameter being estimated' is the correct choice. This concept is a fundamental part of inferential statistics, which seeks to draw conclusions about a population based on sample data.

To further clarify, an unbiased statistic does not depend on the sample size, the sincerity of respondents, or the ethical intentions behind using the statistic. These factors are addressed in the other options, but they are not definitions of what makes a statistic unbiased. It is essential for a sample to be representative of the population, which requires all members have an equal likelihood of being chosen, to avoid sampling bias that can lead to incorrect conclusions.