Question

Find the critical values, z-scores, for the following confidence intervals by showing a graph and respective areas:    (Please show all work)

a.) 90% z-scores    b.) 99% t-scores, n=51

Answer 1

Solution :

Given that,

a ) At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z/2 = Z0.05 = 1.645

The critical value = 1.645

b ) n = 51

Degrees of freedom = df = n - 1 = 51 - 1 = 50

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2,df = t0.005,50 = 2.679

The critical value = 2.679