Which of the following options are true about the use of cen

Which of the following options are true about the use of central limit theorem

It is useful to find the mean and variance of sample mean when we have less than 30 subjects in the sample.

It is useful to construct a confidence interval for sample mean when we have 30 or more subjects in the sample

it is useful to find the approximate sampling distribution of sample mean when have 30 or more subjects in the sample

.It is useful to construct a confidence interval for population mean approximately when we have 30 or more subjects.

it is useful to know that sample mean is same as population mean when we have 30 or more subjects in the sample.

it is useful to find the mean and variance of sample mean when we have 30 or more subjects in the sample.

Solution

Both of

It is useful to construct a confidence interval for population mean when we have 30 or more subjects in the sample

It is useful to find the approximate sampling distribution of population mean when have 30 or more subjects in the sample

because when the sample size is greater the 30, the sampling distribution is approximately normal.

The other choices don\'t make sense. One can\'t find a confidence interval for the sample mean because it is exactly known. Also, one can always calculate the sample mean (if n >= 1) and variance (if n >= 2).