1. Find the critical value ?)

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 size24.

?) ta/z 2 , for a 90% confidence level and for a sample of size39.

Answer:

Solution :Given that,

a) At 96% confidence level

= 1 – 96%  

= 1 – 0.96 =0.04

/2= 0.02Z/2= Z0.02  = 2.054

b) At 99.5% confidence level

= 1 – 99.5%  

= 1 – 0.995 =0.005

/2= 0.0025Z/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= 0.01t/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= 0.05t/2,df= t0.05,38 = 1.686


 
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