The fan blades on commercial jet engines must be replaced when wear on these parts indicates too much variability to pass inspection. If a single fan blade broke during operation, it could severely...

The fan blades on commercial jet engines must be replaced when wear on these parts indicates too much variability to pass inspection. If a single fan blade broke during operation, it could severely endanger a flight. A large engine contains thousands of fan blades, and safety regulations require that variability measurements on the population of all blades not exceed σ²
= 0.18 mm². An engine inspector took a random sample of 81 fan blades from an engine. She measured each blade and found a sample variance of 0.27 mm². Using a 0.01 level of significance, is the inspector justified in claiming that all the engine fan blades must be replaced?