statistics question

Question

) A statistician prepares to calculate a confidence interval. Under what circumstances must the statistician use the t-table as opposed to the Z-table? Show all work and calculation please!

Answer 1

If the population standard deviation is unknown or the sample size is less than 30, then the t-table must be used.

Answer 2

Do you know the population standard deviation?

No -> Use the T Table

Yes -> Is the sample size greater than 30?

No - > Use the T Table

Yes -> Use the Z Table

(T Table converges to Z Table as the degree of freedom increases)

Also, you will use positive or negative Z-Table based on whether your Z-Score is positive or negative. See both tables here https://www.ztable.net/

And similarly you also need to pay attention to whether your t-test is one-tailed or two-tailed when using the Student's T Table. See here: https://www.tdistributiontable.com/