Critical Value

Question

Find the critical value z_a/2 that corresponds to the given confidence level. 90% 

(round to two decimal places as needed) 

Answer 1

To find this value, first find α. Remember that confidence level=1-α. Thus, 0.90=1-α and we get α=0.10. Therefore α/2=0.05. To find the critical value associated with this we can either use a table or the calculator (TI-83/84).

 

Using the table: Since we have α/2 on the left and right sides, we have 0.05 on the left and right. Thus, the area to the left at the critical value will be 0.95 (since we have 0.05 in the outside right tail). Using a table we easily find this value to be exactly between 1.64 and 1.65. This gives us 1.645 which rounds to 1.65.

 

Using a TI-83/84 calculator we use InvNorm(area to the LEFT,0,1) to find this value. InvNorm can be found by pressing 2nd, VARS (will have DISTR written above). Input InvNorm(0.95,0,1) and we get 1.65.