What does it mean to say that the sample mean is an unbiased estimator of the population mean?
A)The sample means will vary minimally from the population mean.
B)The sampling distribution of possible sample means is approximately normally distributed,regardless of the shape of the distribution in the population.
C)If we select a sample at random,then on average we can expect the sample mean to equal the population mean.
D)all of the above

Question

Quizplus · Accepted Answer

An unbiased estimator is one that on average gives the correct estimation of the population parameter. In this case, the sample mean is an unbiased estimator of the population mean as it is equally likely to underestimate or overestimate the population mean, meaning that on average it will be equal to the population mean. Therefore, choice C is the best answer. Choices A and B are related to the variability and distribution of the sample means, but they do not directly address the unbiasedness of the estimator. Choice D is incorrect because choice A and B alone do not necessarily imply unbiasedness.

What Does It Mean to Say That the Sample Mean