Question

A population has a normal distribution. A sample of size n is selected from this population. Describe the shape of the sampling distribution of the sample mean for the following case. n=18

Answer 1

As population is normal, so sample mean is normally distributed when n=18 because central limit theorem is required when parent population is not normal.

We know that if X follows then

.

The mean of sample mean is population mean.

i.e.

When the population from which samples are drawn is normally distributed, then the shape of the sample distribution of is also normally distributed. There are not any effect of sample size on mean of sample mean. i.e. no matter what sample size is.

In above cases (n=18) the shape of the sampling distribution of the sample mean does not change.

sample mean is .