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:

Reaction Formation

A defense mechanism where an individual unconsciously replaces unacceptable impulses with their opposites.

Forbidden Impulse

A desire or thought that is repressed or deemed unacceptable by societal standards or personal conscience, often explored in psychoanalytic theories.

Displacement

A redirection of an impulse from a channel that is blocked into another, more available outlet.

Psychosexual Stages

A theory proposed by Freud describing how personality develops through five stages (oral, anal, phallic, latency, genital) centered on erogenous zones.