estimating mu when sigma is unknown

Question

For a confidence level of 90% with a sample size of 10, find the critical t value.

Answer 1

Assuming a 2 tailed t-test, area to the left of the lower critical value will be 0.05 (1 - 0.90)/2 with

10 - 1 = 9 degrees of freedom

On a TI-84

2nd vars

InvT

area = 0.05

df = 9

giving critical t value of -1.833

(so your critical t values are + and - 1.833)

Answer 2

For a 90% confidence level and sample size 10 we look at the t-value corresponding to the upper 0.05 probability and 9 degrees of freedom = 1.833.