Question

As the sample size increases, the variation of the sample mean from the population mean becomes larger and larger

True/False

Answer 1

False

Explanation:

As per central limit theorem we have for large sample sizes randomly drawn the sample mean will follow a normal distribution, irrespective of the original distribution.

Thus x bar sample mean follows a normal distribution for larger sample sizes randomly drawn.

The mean of sample mean = sample mean itself

Std deviation of sample mean

= Std error of sample mean

=
`(std dev)/(√(n) )`

where n represents the sample size.

Thus variation is inversely proportional to the square root of n.

Hence whenever sample size increases, the variation of the sample mean

will become smaller and smaller.

The given statement is false.