Question #333675

The yield of a chemical process is being studied. From a previous experience yield is known to be normally distributed and σ = 3. The past 5 days if plant operation have to resulted in the following percent yields: 91.6,88.75,90.8,89.95, and 91.3. Find a 95% two-sided confidence interval on the true mean yield.

1
Expert's answer
2022-04-28T15:46:03-0400

Sample mean

xˉ=15(91.6+88.75+90.8+89.95+91.3)=90.48\bar{x}=\dfrac{1}{5}(91.6+88.75+90.8+89.95+91.3)=90.48

 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}})

=(90.481.96×35,90.48+1.96×35)=(90.48-1.96\times\dfrac{3}{\sqrt{5}}, 90.48+1.96\times\dfrac{3}{\sqrt{5}})

=(87.85,93.11)=(87.85, 93.11)

Therefore, based on the data provided, the 95% confidence interval for the population mean is 87.85<μ<93.11,87.85 < \mu < 93.11, which indicates that we are 95% confident that the true population mean μ\mu is contained by the interval (87.85,93.11).(87.85, 93.11).


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS