Question #337204

A sample of 20 observations is selected from normal population distribution with

population standard deviation 9 and sample mean 51. Determine the highest

value of population mean with 95% confidence interval (z-1.96). Round the

answer to the two decimal places.


1
Expert's answer
2022-05-05T06:47:59-0400

The critical value for α=0.05\alpha = 0.05 is zc=z1α/2=1.96.z_c = z_{1-\alpha/2} = 1.96.

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}})

=(511.96×920,51+1.96×920)=(51-1.96\times\dfrac{9}{\sqrt{20}}, 51+1.96\times\dfrac{9}{\sqrt{20}})

=(47.06,54.94)=(47.06, 54.94)

The highest value of population mean with 95% confidence interval is 54.94.54.94.



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