Question

1. Find the critical value

?) ??/z 2 , for a 96% confidence level.

?) ??/z 2 , for a 99.5% confidence level.

?) ??/z 2 , for a 98% confidence level and for a sample of size 24.

?) ta/z 2 , for a 90% confidence level and for a sample of size 39.

Answer 1

Solution :

Given that,

a) At 96% confidence level

= 1 - 96%  

= 1 - 0.96 =0.04

/2 = 0.02

Z/2 = Z0.02  = 2.054

b) At 99.5% confidence level

= 1 - 99.5%  

= 1 - 0.995 =0.005

/2 = 0.0025

Z/2 = Z0.0025  = 2.81

c) sample size = n = 24

Degrees of freedom = df = n - 1 = 24 - 1 = 23

At 98% confidence level

= 1 - 98%

=1 - 0.98 =0.02

/2 = 0.01

t/2,df = t0.01,23 = 2.500

d) sample size = n = 39

Degrees of freedom = df = n - 1 = 39 - 1 = 38

At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

/2 = 0.05

t/2,df = t0.05,38 = 1.686