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

Trent Carpenter 2021-01-15 Answered
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 (?, ?)
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Expert Answer

Asma Vang
Answered 2021-01-16 Author has 93 answers

Step 1 Solution: We need to construct the 99% confidence interval for the population variance. We have been provided with the following information about the sample variance and sample size: s2=1369
n=20 Step 2 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 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) =(674.17,3800.5711)=(25.9648,61.6488) Therefore, based on the data provided, the 99% confidence interval for the population variance is 674.17<σ2<3800.5711, and the 99% confidence interval for the population standard deviation is 25.9648<σ<61.6488. Step 3 Ci for population variance (674.17 , 3800.57) Ci for population standard deviation ( 25.96 , 61.65)

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