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A new catalyst is being investigated for use in the production of a plastic chemical. Ten...

A new catalyst is being investigated for use in the production of a plastic chemical. Ten batches of the chemical are produced. The mean yield of the 10 batches is 72.5% and the standard deviation is 5.6%. Assume the yields are independent and approximately normally distributed. Find a 99% confidence interval for the mean yield when the new catalyst is used. Round the answers to three decimal places.

The 99% confidence interval is (  ,  ).

math   Statistics-And-Probability   
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Answer #1

We have given that,                  
                  
Sample mean =72.5%          
Sample standard deviation =5.6%  
Sample size =10          
Level of significance=1-0.99=0.01          
Degree of freedom =9          
                  
t critical value is (by using t table)=3.25          

\bar{x}\pm t*\frac{S}{\sqrt{n}}= 72.5 \pm 3.25 *(\frac { 5.6 } {\sqrt{ 10 }})=( 66.745 , 78.255 )
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