In: Statistics and Probability
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.
22 | 17 | 29 | 35 | 43 | 25 | 25 | 25 |
Calculate a 99% CI for the standard deviation of the coating layer thickness distribution. (Round your answers to two decimal places.)
We have for given data,
Sample variance =65.411
Sample standard deviation=8.09
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=0.989
Chi square critical value for upper tail=20.278
We can use here confidence interval formula for population standard
deviation
=(4.75,21.52)
Lower confidence limit for population standard
deviation=4.75
Upper confidence limit for Population standard
deviation=21.52