Question

True of False

the sampling distribution of a parameter is the distribution of the parameter value if repeated random samples are obtained

The central lmit theorem is important in statistics because for a large random sample, it says the sampling distribution of the sample mean is approximately normal

Answer 1

Solution:

1) The sampling distribution of a statistic is the probability distribution of the statistic derived from the repeated random samples of size n.

But in the given statement the term used is "sampling distribution of a parameter" which is not correct. Always we derive sampling distribution of a statistic and not for the parameter. A parameter is used in the context of population whereas for sample we use statistic.

Hence, in the given statement everything is right but the word "statistic" must be used in place of parameter.

2) The central limit theorem says that if we have a population with mean μ and variance σ^{​​​​​​2} and we take a large sample from this population then sampling distribution of sample mean will be approximately normal.

Hence, the statement "The central lmit theorem is important in statistics because for a large random sample, it says the sampling distribution of the sample mean is approximately normal" is True.