Question

In: Statistics and Probability

Wire electrical-discharge machining (WEDM) is a process used to manufacture conductive hard metal components. It uses...

Wire electrical-discharge machining (WEDM) is a process used to manufacture conductive hard metal components. It uses a continuously moving wire that serves as an electrode. Coating on the wire electrode allows for cooling of the wire electrode core and provides an improved cutting performance. An article gave the following sample observations on total coating layer thickness (in µm) of eight wire electrodes used for WEDM.

21 17 29 35 43 25 24 26

Calculate a 99% CI for the standard deviation of the coating layer thickness distribution.

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Solutions

Expert Solution

We have given here,                                              
                                              
                                      
Sample standard deviation=8.212                              
Sample size =8                                      
                                              
Degree of freedom =n-1=   7                                  
Level of significance given =1-0.99=0.01                                  
Chi square critical value for lower tail=0.9893   .......by using =CHIINV(1-(0.01/2),7)                          
                                              
Chi square critical value for upper tail=20.2777.........by using =CHIINV((0.01/2),7)                          
                                              
We can use here confidence interval formula for population standard deviation


=(4.82,21.84)                                              
                                              
                                              
                                              
                      
                                              
Lower confidence limit for population standard deviation=4.82                  
                                              
Upper confidence limit for Population standard deviation=21.84  


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