Question

The Central Limit Theorem says the sampling distribution of the sample mean is approximately normal under certain conditions. Which of the following is a necessary condition for the central Limit Theorem to be used?

a) The population from which we are sampling must be normally distributed.
b ) The population size must be large (e.g. , at least 30)
c) The sample size must be large (e.g., at least 30)
c) The population from which we are sampling must not be normally distributed.

Answer 1

c) The sample size must be large (e.g., at least 30)

Explanation:

Central Limit theorem states that : If population has well defined & finite mean & variance, even if it is skewed - the sampling distribution of sample mean will tend to 'normal distribution', as the number of samples increase.

The sampling distribution shape will approach to 'normality' as sample size (N) increase. The sample size must be atleast 30 for this case.

Answer 2

Option C

Explanation:

The central Limit Theorem says the sampling distribution of the sample mean is approximately normal under certain conditions

The conditions are

i) the population should be symmetrial. If population is skewed sample size should be sufficiently large atleast 30

ii) Samples should be drawn strictly at random

iii) the sample observations should be independent

Thus we find that option a is not necessary because even for skewed large sample size allows the theorem

Option b is not correct since if population is less than 30, sampling itself is not necessary.

Option d is also wrong since normality is not necessary

Only option C) The sample size must be large (e.g., at least 30) is the necessary condition