Question

Question 14 True or false? Even with small sample sizes (eg, 15 people), the sampling distribution will always be normally distributed True False

Answer 1

Solution:

Central limit theorem state that for large sample size, when independent random variables are added, their properly normalized sum tends toward a normal distribution.

In order for the result of the CLT to hold, the sample must be sufficiently large (n > 30). Again, there are two exceptions to this. If the population is normal, then the result holds for samples of any size (i..e, the sampling distribution of the sample means will be approximately normal even for samples of size less than 30).

If the population is normal, then the theorem holds true even for samples smaller than 30.

Therefore, this is a FALSE statement.

even with the small sample size, the sampling distribution will not always be normally distributed.