Artificial Hip Joints Consist of a Ball and Socket $\begin{array}{ccccc}\hline \text { Diameter } & {\text { Head Roughness }} \\\hline 16 & 20.9 & 20.0 & 31.4 & 24.8 \\24 & 32.6 & 28.0 & 36.5 & \\30 & 19.0 & 19.3 & 29.8 & \\\hline\end{array}$

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).
$\begin{array}{ccccc}\hline \text { Diameter } & {\text { Head Roughness }} \\\hline 16 & 20.9 & 20.0 & 31.4 & 24.8 \\24 & 32.6 & 28.0 & 36.5 & \\30 & 19.0 & 19.3 & 29.8 & \\\hline\end{array}$
i). Construct an ANOVA table.
ii). Can you conclude that the mean roughness varies with diameter? Use the $\alpha = \mathrm { C }$ level of significance.

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