Answer to Question #169483 in Statistics and Probability for Sunera

Question #169483

Suppose that a random sample of five observations was taken from a normal population whose variance is 25. The results are 8, 15, 12, 6, 7. Find the 99% confidence interval estimate of the population mean.


1
Expert's answer
2021-03-16T02:40:35-0400

n=5,σ2=25n=5, \sigma^2=25

Sample mean


Xˉ=8+15+12+6+75=9.6\bar{X}=\dfrac{8+15+12+6+7}{5}=9.6

Standard deviation


σ=σ2=25=5\sigma=\sqrt{\sigma^2}=\sqrt{25}=5

The critical value for α=0.01\alpha=0.01 is zc=z1α/2=2.576.z_c=z_{1-\alpha/2}=2.576.

The corresponding confidence interval is computed as shown below:


CI=(Xˉzc×σn,Xˉ+zc×σn)CI=(\bar{X}-z_c\times \dfrac{\sigma}{\sqrt{n}},\bar{X}+z_c\times \dfrac{\sigma}{\sqrt{n}})

=(9.62.576×55,9.6+2.576×55)=(9.6-2.576\times \dfrac{5}{\sqrt{5}},9.6+2.576\times \dfrac{5}{\sqrt{5}})

=(3.84,15.36)=(3.84,15.36)


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