# Thread: Z versus t statistic for small sample sizes?

1. ## Z versus t statistic for small sample sizes?

For relatively small sample sizes such as 20, when given a sample mean and sample standard deviation, and only knowing that the variable is approximately normally distributed but the true standard deviation is unknown, can we create a t or Z statistic? What is more important in assuming normality, the sample size or knowing a standard deviation? Does the answer change based upon whether the mean and standard deviation that might be used for comparison in hypothesis testing are known and are normal? Thanks, Jenna

2. Originally Posted by jennagreer
For relatively small sample sizes such as 20, when given a sample mean and sample standard deviation, and only knowing that the variable is approximately normally distributed but the true standard deviation is unknown, can we create a t or Z statistic? What is more important in assuming normality, the sample size or knowing a standard deviation? Does the answer change based upon whether the mean and standard deviation that might be used for comparison in hypothesis testing are known and are normal? Thanks, Jenna
If you know that the distribution is normal, and the SD is known, then the sample mean has a normal distribution no matter what the sample size.

If you know the distribution is normal but SD is unknown and has to be estimated form the sample then we need the t-distribution.

CB