1. Find the critical value ?)
January 18th, 2023
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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