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). Can you conclude that the mean roughness varies with diameter? Use the $\alpha = 0.05$ level of significance.

Question

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).  Can you conclude that the mean roughness varies with diameter? Use the $\alpha = 0.05$ level of significance.

Quizplus · Accepted Answer

To test if the mean roughness varies with diameter, we need to perform an ANOVA (Analysis of Variance) test. Since we are given the significance level ($\alpha=0.05$), we can use it as the level of significance for our test. Conducting the ANOVA test on the data will give us an F-statistic and a p-value. If the p-value is less than our significance level, we can reject the null hypothesis and conclude that there is a significant difference in mean roughness between the groups with different diameters. Without the data or the test results, we cannot calculate the p-value or make a definitive conclusion.

Artificial Hip Joints Consist of a Ball and Socket α=0.05\alpha = 0.05α=0.05

Artificial Hip Joints Consist of a Ball and Socket $\alpha = 0.05$