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 these.

Question

Quizplus · Accepted Answer

Saying that the sample mean is an unbiased estimator of the population mean means that if we select a sample at random, then on average we can expect the sample mean to equal the population mean. This means that the sample means won't be systematically over or underestimating the population mean. Option A is incorrect because the sample means can vary from the population mean, but they won't be systematically biased. Option B is incorrect because the normality assumption only holds for large sample sizes (Central Limit Theorem), and it's not always true regardless of the shape of the population distribution.

What Does It Mean to Say That the Sample Mean