Use technology to construct the confidence intervals for the population variance sigma^{2} and the population standard deviation sigma. Assume the sam

Trent Carpenter

Trent Carpenter

Answered question

2021-01-15

Use technology to construct the confidence intervals for the population variance σ2 and the population standard deviation σ. Assume the sample is taken from a normally distributed population. c=0.99,s=37,n=20 The confidence interval for the population variance is (?, ?). The confidence interval for the population standard deviation is (?, ?)

Answer & Explanation

Asma Vang

Asma Vang

Skilled2021-01-16Added 93 answers

Step a 

Solution: The 99% confidence interval for the population variance must be built. The following details concerning sample variation and sample size have been sent to us: s2=1369
n=20 Step b 

The critical values for α=0.01 and df=19 degrees of freedom are XL2=X1α2,n12=6.844 and XU2=X1α2,n12=38.5823. The corresponding confidence interval is computed as shown below: CI(Variance)=((n1)s2Xα2,n12,(n1)s2X1α2,n12)
((201)×136938.5823,(201)×13696.844 
=(674.17,3800.5711) Now that we have the upper and lower bounds of the confidence interval, we can easily calculate the lower and upper bounds of the 99% confidence interval for the population standard deviation by taking the square root of the upper and lower bounds of the confidence interval for variance.

 CI(Standard Deviation) =(674.17,3800.5711)=(25.9648,61.6488) The 99% confidence range for the population variance, then, based on the presented data, is674.17<σ2<3800.5711, and the 99% confidence interval for the population standard deviation is 25.9648<σ<61.6488

Step 3 A population variance index (CI) (674.17 , 3800.57) Population standard deviation coefficient ( 25.96 , 61.65)

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