Question

Which of the following is a true statement for any population with mean μ and standard deviation σ? I. The distribution of sample means for sample size n will have a mean of μ. II. The distribution of sample means for sample size n will have a standard deviation of. III. The distribution of sample means will approach a normal distribution as n approaches infinity.

Answer 1

Answer:

Which of the following is a true statement for any population with mean μ and standard deviation σ?

I.The distribution of sample means for sample size n will have a mean of μ.

True

II. The distribution of sample means for sample size n will have a

.standard deviation of σ/sqrt(n)    true

OR

standard deviation of σ   false

III. The distribution of sample means will approach a normal distribution as n approaches infinity.

True

Note:

The central limit theorem states that if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population is taken , then the distribution of the sample means will be approximately normally distributed with mean μ and standard deviation σ/sqrt(n).