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 61 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?
Please provide the following information:
(a) What is the level of significance? State the null and alternate hypotheses.
(b) Find the value of the chi-square statistic for the sample. What are the degrees of freedom? What assumptions are you making about the original distribution?
(c) Find or estimate the P-value of the sample test statistic.
(d) Based on your answers in parts (a)–(c), will you reject or fail to reject the null hypothesis of independence?
(e) Your conclusion in the context of the application.