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Artificial Hip Joints Consist of a Ball and Socket Can You Conclude That the Mean Roughness Varies with Diameter

question 115

True/False

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).
 Diameter  Head Roughness 1627.521.427.426.32430.235.633.83024.921.225.5\begin{array}{ccccc}\hline \text { Diameter } & {\text { Head Roughness }} \\\hline 16 & 27.5 & 21.4 & 27.4 & 26.3 \\24 & 30.2 & 35.6 & 33.8 & \\30 & 24.9 & 21.2 & 25.5 & \\\hline\end{array}
Can you conclude that the mean roughness varies with diameter? Use the α=0.01\alpha = 0.01 level o significance.

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