When to use the t distribution?

When to use the t distribution?

On pg 333, chapter 8, question 22, the sample size is less than 30, the SD is unknown, but in part (B) of the question it says "the population has a normal distribution".

So should you use the T distribution or normal distribution? Go for the T dist because the standard deviation is unknown. So, even if the population is normally distributed, if you don’t know its standard deviation, use the T. In fact I always use the T distribution in applied (real) work. It is safer, giving you a wider margin or error and therefore confidence interval. Therefore the chances of rejecting a true null (and therefore making a Type 1 error are smaller. Nice question, thanks RB.

Note that you should be able to find confidence intervals using the normal distribution and for the t-distribution  using the Data Analysis> Descriptive Stats. There is a Youtube here

Point to note: don't mix up the Margin of Error and the Confidence Interval. We need to find the Margin of Error to create the Confidence Interval. The Confidence Interval is the sample mean (xbar) plus/minus the Margin of Error.