Question

Samples A and B were selected from the same population. The mean of sample A is equal to the mean of the population. Which of the following statements must be true? I. The mean of sample A is a point estimator for the mean of the population. II. The mean of sample B is a point estimator for the mean of the population. III. The mean of sample A is equal to the mean of sample B.

a. I only b. II only c. III only d. I and II e. II and III

Answer 1

The sample means of both A and B are point estimators for the population mean, making option d (I and II) correct. We cannot assume that the sample means of A and B are equal without more information.

Step-by-step explanation:

The question pertains to statistics and the concept of point estimators. When a sample mean equals the population mean, this sample mean is acting as a point estimator for the population mean. This makes statement I true because the mean of sample A can be used as a point estimator of the population mean. Statement II is generally true because any sample mean (including sample B's mean) is considered a point estimator for the population mean as well, irrespective of whether it is equal to or different from the population mean. However, statement III cannot be assumed to be true without additional information, as we do not know whether sample A's mean is equal to sample B's mean just because sample A's mean equals the population mean.

The correct answer to the initial question therefore is option d (I and II).