Find the length of the confidence interval given the following

midtlinjeg

midtlinjeg

Answered question

2021-09-20

Find the length of the confidence interval given the following data: (s-sample standard deviation)
a) s=2.36
n=350
confidence level: 99% b) s=3.35
n=250
confidence level: 99%
c) s=3
n=275
confidence level: 95%

Answer & Explanation

tafzijdeq

tafzijdeq

Skilled2021-09-21Added 92 answers

Step 1
a) We have been provided with the following information about the sample variance and sample size:
s=5
s2=25
n=350
The critical values for α=0.01 and df=349 degrees of freedom are χL2=χ1α2, n12=284.7055 and χU2=χα2, n12=420.803. The corresponding confidence interval is computed as shown below:
CI(Variance)=((n1)s2χα2, n12, (n1)s2χ1α2, n12)
=((3501)×25420.803, (3501)×25284.7055)
=(20.7342, 30.6457)
Now that we have the limits for the confidence interval, the limits for the 99% confidence interval for the population standard deviation are obtained by simply taking the squared root of the limits of the confidence interval for the variance, so then:
CI(Standard Deviation)=(20.7342, 30.6457=(4.5535, 5.5359)
Length =5.5354.553=0.982
Step 2
b) s=3.35
s2=11.2225
n=250
The critical values for α=0.01 and df=249 degrees of freedom are χL2=χ1α2, n12=195.2759 and χU2=χα2, n12=310.2308. The cprresponding confidence interval is computed as shown below. NKS CI(Variance)=((n1)s2χα2, n12,(n1)s2χ1α2, n12)

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