Question

Surface roughness of steel is investigated. The method of surface manufacturing largely determines roughness of the surface. One of the parameters to describe the roughness is Rz, the maximum height of the surface irregularities profile. Rz (in μm) is measured for 21 random places on the surface of forged details and 21 random places on the surface of casted details. Is there evidence to support the claim that the surface of forged steel has a larger surface roughness variance than the surface of casted details?

Forge	Cast
102	105
82	99
94	97
117	105
94	96
105	101
88	90
92	104
90	92
81	106
102	104
96	104
88	90
80	104
105	107
101	91
90	92
110	89
91	93
110	105
94	96

Answer 1

Solution:

Null hypothesis; H0: The surface of forged steel has a same surface roughness variance as the surface of casted details.

Alternative hypothesis: Ha: The surface of forged steel has a larger surface roughness variance than the surface of casted details.

Test statistic is given as below:

F = S1^2/S2^2

From given data, we have

S1^2 = 101.0619048

S2^2 = 40.15714286

F = 101.0619048/40.15714286

F = 2.5167

Df1 = n1 - 1 = 21 - 1 = 20

Df2 = n2 - 1 = 21 - 1 = 20

P-value = 0.0225 < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the surface of forged steel has a larger surface roughness variance than the surface of casted details.