Question

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

16

29

35

42

24

24

25

Calculate a 99% CI for the standard deviation of the coating layer thickness distribution. (Round your answers to two decimal places.)

Answer 1

Mean X̅ = Σ Xi / n
X̅ = 217 / 8 = 27.125
Sample Standard deviation SX = √ ( (Xi - X̅ )2 / n - 1 )
SX = √ ( 460.8748 / 8 -1 ) = 8.1141

(0.01/2, 8 - 1 ) = 20.2777
(1 - 0.01/2, 8 - 1) ) = 0.9893
Lower Limit = 4.77
Upper Limit = 21.58
99% Confidence interval is ( 4.77 , 21.58 )
( 4.77 < σ < 21.58 )