Artificial Hip Joints Consist of a Ball and Socket I) Construct an ANOVA Table

question 24

Essay

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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Definitions:

Divergent Plate Boundary

A tectonic margin where two lithosphere plates are moving apart from each other, typically resulting in the formation of new oceanic crust through volcanic activity.

Volcanic Eruptions

Explosive events where molten rock (magma), ash, and gases are ejected from a volcano's vent, impacting the surrounding environment and climate.

Landslides

The movement of rock, earth, or debris down a slope due to gravity, often precipitated by factors like water saturation, erosion, or earthquakes.

Magma Movement

The flow or migration of magma through the Earth's crust, which can lead to volcanic eruptions when it reaches the surface.