Artificial hip joints consist of a ball and socket.

As the joint wears, the ball (head) becomes rough. Investigators performed wear tests on metal artificial hip joints. Joints with several different diameters were tested. The following table presents measurements of head roughness (in nanometers).

a. Because the design is unbalanced, check that the assumption of equal variances is satisfied by showing that the largest sample standard deviation is less than twice as large as the smallest one.

b. Construct an ANOVA table.

c. Can you conclude that mean roughness varies with diameter? Use the α = 0.01 level of significance.

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Diameter Head Roughness 16 0.83 2.25 0.40 2.78 3.23 28 2.72 2.48 3.80 36 6.49 5.32 4.59