Since the sample size is always smaller than the size of the

Since the sample size is always smaller than the size of the population, the sample mean:

must always be smaller than the population mean

must be larger than the population mean

must be equal to the population mean

can be smaller, larger, or equal to the population mean

The central limit theorem tells us that the sampling distribution of the sample mean is approximately normal. Which of the following conditions are necessary for the theorem to be valid:

a) The sample size has to be large.

b) We have to be sampling from a normal population.

c) The population has to be symmetric.

d) Both a) and c).

A simple random sample from an infinite population is a sample selected such that:

each element is selected independently and from the same population

each element has a 0.5 probability of being selected

each element has a probability of at least 0.5 of being selected

the probability of being selected changes

Solution

Since the sample size is always smaller than the size of the population, the sample mean:

can be smaller, larger, or equal to the population mean

The central limit theorem tells us that the sampling distribution of the sample mean is approximately normal. Which of the following conditions are necessary for the theorem to be valid:

The sample size has to be large.

A simple random sample from an infinite population is a sample selected such that:

each element is selected independently and from the same population