11.38 Heat treating is often used to carburize metal parts such as gears. The thickness of the carburized layer is considered an important feature of the gear, and it contributes to the overall reliability of the part.

Because of the critical nature of this feature, a lab test is performed on each furnace load. The test is a destructive one, where an actual part is cross sectioned and soaked in a chemical for a period of time. This test involves running a carbon analysis on the surface of both the gear pitch (top of the gear tooth) and the gear root (between the gear teeth). The data below are the results of the pitch carbon-analysis test for 19 parts.

Soak Time Pitch Soak Time Pitch 0.58 0.013 1.17 0.021 0.66 0.016 1.17 0.019 0.66 0.015 1.17 0.021 0.66 0.016 1.20 0.025 0.66 0.015 2.00 0.025 0.66 0.016 2.00 0.026 1.00 0.014 2.20 0.024 1.17 0.021 2.20 0.025 1.17 0.018 2.20 0.024 1.17 0.019

(a) Fit a simple linear regression relating the pitch carbon analysis y against soak time. Test H0: β1 = 0.

(b) If the hypothesis in part

(a) is rejected, determine if the linear model is adequate.