Question

Answer the following questions. (a) Why do we need to use the t-distribution when estimating the population mean? (b) Name a circumstance where we would not need to use the t-distribution when estimating the population mean?

Answer 1

a) when the sample size is small (n<30) then t-test can estimate mean better than z-test with high power of the test so, we use exact t-test to estimate the mean of a population.

b)

When sample size is large then on that case due to central limit theorem the distribution used is normal.

When the parent population from which the sample is drawn is not normal.

When the sample is not random.

When the standard deviation sigma is known.

In all the above circumstances we would need not to use t-distribution.