help with part of a question

Question

You take a sample of 22 from a population of test scores, and the mean of your sample is 60.

You know the standard deviation of the population is 10. What is the 99% confidence interval on the population mean?

I got:
60 + 2.58 * (10/ √22)
= 60 +1.172727√22
= 65.501

60 - 2.58 * (10/ √22)
= 60 -1.172727√22
= 54.499

Answers:
(54.499, 65.501)


Now assume that you do not know the population standard deviation, but the standard deviation in your sample is 10. What is the 99% confidence interval on the mean now?

this is the part that i need help with. I cant find anything talking about it in my notes and i have no idea how i would solve this one.

Answer 1

With an unknown population variance you can use the sample as an approximation but instead of using a normal distribution use a t distribution with the appropriate degrees of freedom.