Question

True or False?

The sampling distribution of the sample mean of a non-normally distributed population will also be normally distributed as long as the sample size is greater than 10.

The sampling distribution of the sample mean of a normally distributed population will not be normally distributed if sample size is less than 30.

Answer 1

FALSE. According to central limit theorem ...we can approximate the mean of a non-normally distributed population by a normal distribution if the sample size n is adequately large. Sample size of 10 is not always adequate .for example a random sample of size 10 from a binomial distribution can only be approximated by a normal distribution if the probability of success (p) is 1/2 . If p is grater than or less than 1/2 we need a larger sample size. There are a no of ways to determine the required sample size for normal approximation.

FALSE. The sampling distribution of any linear function (like sample mean) of a normally distributed population wil always be normally distributed.