In: Statistics and Probability
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.
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