A consistent estimator for the mean:
A)converges on the true parameter μ as the variance increases.
B)converges on the true parameter μ as the sample size increases.
C)consistently follows a normal distribution.
D)is impossible to obtain using real sample data.

Question

Quizplus · Accepted Answer

As the sample size increases, the estimator becomes more precise and has smaller variance. Therefore, with a larger sample size, the estimator converges on the true parameter μ. This is known as the law of large numbers. Option A is incorrect as increasing variance does not necessarily improve the accuracy of the estimator. Option C is incorrect as the estimator's distribution is not always normal. Option D is incorrect as the sample mean is a common estimator for the population mean and is obtainable using real sample data.

A Consistent Estimator for the Mean