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Artificial Hip Joints Consist of a Ball and Socket Perform the Tukey-Kramer Test to Determine Which Pairs of Means

question 28

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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 1619.825.917.523.22431.933.027.73026.628.821.2\begin{array}{ccccc}\hline \text { Diameter } &{\text { Head Roughness }} \\\hline 16 & 19.8 & 25.9 & 17.5 & 23.2 \\24 & 31.9 & 33.0 & 27.7 & \\30 & 26.6 & 28.8 & 21.2 & \\\hline\end{array}
Perform the Tukey-Kramer test to determine which pairs of means, if any, differ. Use the α=0.05\alpha = 0.05 level of significance.

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Definitions:

Unit Selling Price

The price at which a single unit of a product is sold to customers.

Unit Variable Cost

The cost that varies with each unit produced, including materials, labor, and other expenses directly tied to production volume.

Minimum Required Rate Of Return

This is the lowest acceptable return on an investment, determined by the investor's risk tolerance, inflation expectations, and the opportunity cost of capital.

Total Fixed Costs

The sum of all costs that do not change with the level of production or sales over a certain period, such as rent, salaries, and insurance.

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