In: Statistics and Probability
sample std dev , s = 45.0612
Sample Size , n = 31
Sample Mean, x̅ = 94.6129
degree of freedom= DF=n-1= 30
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95% confidence interval for population mean
α = 1-0.95 = 0.05
't value=' tα/2= 2.0423
[Excel formula =t.inv(α/2,df) ]
Standard Error , SE = s/√n =
8.0932
margin of error , E=t*SE =
16.529
confidence interval is
Interval Lower Limit= x̅ - E =
78.08
Interval Upper Limit= x̅ + E =
111.14
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99% confidence interval for population mean
α=1-0.99 = 0.01
't value=' tα/2= 2.7500
[Excel formula =t.inv(α/2,df) ]
Standard Error , SE = s/√n =
8.0932
margin of error , E=t*SE =
22.256
confidence interval is
Interval Lower Limit= x̅ - E =
72.36
Interval Upper Limit= x̅ + E =
116.87
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95% confidence intervals of the standard devaition
Sample Size, n= 31
Sample Standard Deviation, s= 45.0612
Confidence Level, CL= 95%
Degrees of Freedom, DF=n-1 = 30
alpha, α=1-CL= 0.05
alpha/2 , α/2= 0.025
from chi square table,
Lower Chi-Square Value= χ²1-α/2
= 16.7908
Upper Chi-Square Value= χ²α/2 =
46.9792
95% confidence interval for std dev is
lower bound= √[ (n-1)s²/χ²α/2 ] =
36.0089
upper bound= √[ (n-1)s²/χ²1-α/2 ] = 60.2321
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99% confidence intervals of the standard devaition
Sample Size, n= 31
Sample Standard Deviation, s=
45.0612
Confidence Level, CL= 99%
Degrees of Freedom, DF=n-1 = 30
alpha, α=1-CL= 0.01
alpha/2 , α/2= 0.005
Lower Chi-Square Value= χ²1-α/2
= 13.7867
Upper Chi-Square Value= χ²α/2 =
53.6720
confidence interval for std dev is
lower bound= √[
(n-1)s²/χ²α/2 ] = 33.6891
upper bound= √[ (n-1)s²/χ²1-α/2 ] = 66.4711