Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 218 / 1 / d / Solution

The null hypothesis isagainst the alternative that at least one coefficient is nonzero. The code uses the scaled reduction in exponential-family deviance,and compares it with ${\chi }_3^2$.

That chi-squared calibration is appropriate when the dispersion is known, and is asymptotically valid after consistent dispersion estimation. With unknown Gamma dispersion, the standard finite-sample GLM comparison instead usesagainst an $F_{3,57}$ distribution. Its p-value is approximately $0.034$, so the correctly calibrated test still rejects at the 5% level and gives evidence that component type or position contributes to mean failure time.