Under what situations would you use tc instead of zc when cr

Under what situations would you use t_c instead of z_c when creating a confidence interval?

Solution

When creating a confidence interval when we are using a sample standard deviation instead of population standard deviation.Basically when standard deviation is not known then we use t critical value and when standard deviation is known we use z critical value

when standard deviation is known then

confidence interval is x bar+- zc sigma/sqrtn

when standard deviation is not known

confidence interval os x bar+- tc *s/sqrtn