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 exceed²= 0.18 mm².An engine inspector took a random sample of81fan blades from an engine. She measured each blade and found a sample variance of0.28mm². Using a 0.01 level of significance, is the inspector justified in claiming that all the engine fan blades must be replaced?

(a) What is the level of significance?

(b) State the null and alternate hypotheses.

• H₀:²= 0.18;H₁:²> 0.18
• H₀:²> 0.18;H₁:²= 0.18
• H₀:²= 0.18;H₁:²< 0.18
• H₀:²= 0.18;H₁:²0.18

(d) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)

(e) What are the degrees of freedom?

(f) What assumptions are you making about the original distribution?

• We assume a binomial population distribution.
• We assume a exponential population distribution.
• We assume a uniform population distribution.
• We assume a normal population distribution.

(g) Find or estimate theP-value of the sample test statistic.

• P-value > 0.100
• 0.050 <P-value < 0.100
• 0.025 <P-value < 0.050
• 0.010 <P-value < 0.025
• 0.005 <P-value < 0.010
• P-value < 0.005

(h) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

• Since theP-value >, we fail to reject the null hypothesis.
• Since theP-value >, we reject the null hypothesis.
• Since theP-value, we reject the null hypothesis.
• Since theP-value, we fail to reject the null hypothesis.

(i) Interpret your conclusion in the context of the application.

• At the 1% level of significance, there is insufficient evidence to conclude that the variance of measurements on the fan blades is higher than the specified amount. The inspector is not justified in claiming the blades must be replaced.
• At the 1% level of significance, there is sufficient evidence to conclude that the variance of measurements on the fan blades is higher than the specified amount. The inspector is justified in claiming the blades must be replaced.
• At the 1% level of significance, there is sufficient evidence to conclude that the variance of measurements on the fan blades is higher than the specified amount. The inspector is not justified in claiming the blades must be replaced.
• At the 1% level of significance, there is insufficient evidence to conclude that the variance of measurements on the fan blades is higher than the specified amount. The inspector is justified in claiming the blades must be replaced.