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:
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).
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