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 71 fan blades from an engine. She measured each blade and found a sample variance of 0.32 mm2. Using a 0.01 level of significance, is the inspector justified in claiming that all the engine fan blades must be replaced?

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okpalawalter8 okpalawalter8 · Answer 1 · 2021-07-19T05:51:33+02:00

Answer:

All the engine fan blades must be replaced

Step-by-step explanation:

From the question we are told that:

Sample size [tex]n=71[/tex]

[tex]\sigma^2 = 0.18 mm2[/tex]

Variance [tex]s^2=0.32[/tex]

Level of significance [tex]\alpha =0.01[/tex]

Generally the hypothesis is

The test hypothesis is

Null [tex]H_0:\sigma^2<=0.18[/tex]

Alternative [tex]Ha:\sigma^2>0.18[/tex]

Generally the equation for Chi distribution is mathematically given by

The test statistic is

[tex]X^2 = \frac{(n-1)*s^2}{\sigma^2}[/tex]

[tex]X^2={70*0.32}{0.18}[/tex]

[tex]X^2= 124.4[/tex]

Since

Critical Value

[tex]C_{\alpha, df}=C_{0.99 , 70}[/tex]

[tex]C_{0.99 , 70} =100.4252[/tex]

Hence, we Reject [tex]H_0[/tex] ,Given that 124.4 is Greater than 100.4252

Therefore

All the engine fan blades must be replaced