Construct 98% confidence intervals for the a) population variance and the b)population standard deviation sigma The number of hours of reserve capacit

permaneceerc 2020-11-08 Answered
Construct 98% confidence intervals for the a) population variance and the b)population standard deviation σ The number of hours of reserve capacity of 10 randomly selected automotive batteries. 1.71, 1.87, 1.58, 1.61, 1.78, 1.98, 1.36, 1.58, 1.47, 2.05, Assume the sample is taken from a normally distributed population.
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Expert Answer

Yusuf Keller
Answered 2020-11-09 Author has 90 answers
Use STDEV function in excel to find the standard deviation. Then, s=0.2215.And the variance iss2=(0.2215)2
=0.04906Step 2At 98% level,α=198%
=10.98
=0.02AndThe degree of freedom =n1
=101
=9Step 3The critical values areX{α,n1}2=X{0.02,9}2
=19.679AndX{1α,n1}2=X{0.98,9}2
=2.5324Step 4The 98% confidence interval for variance is[(n1)s2x{α,n1}2σ2(n1)s2x{1α,n1}2]=9(0.04906)19.679σ29(0.04906)2.5324
=0.4415419.679σ20.441542.5324
=0.022σ20.174The 98% confidence interval for standard deviation is[(n1)s2X{α,n1}2σ(n1)s2X{1α,n1}2]=0.022σ0.174
=0.150σ0.417
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