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

I and III are true.

Explanation:

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

TRUE. The sampling distribution, or the distribution for the sample means of any size n, will have the same mean as the population.

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

FALSE. The standard deviation of the sampling distribution depends on the sample size, with the relation:

`\sigma_s=(\sigma)/(√(n))`

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

TRUE. As the sample size increases, according to the Central Limit Theorem, the sampling distribution will have approximate to a bell-shaped distribution.