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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?

User Leenephi
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1 Answer

17 votes
17 votes

Answer:

All the engine fan blades must be replaced

Explanation:

From the question we are told that:

Sample size
n=71


\sigma^2 = 0.18 mm2

Variance
s^2=0.32

Level of significance
\alpha =0.01

Generally the hypothesis is

The test hypothesis is

Null
H_0:\sigma^2<=0.18

Alternative
Ha:\sigma^2>0.18

Generally the equation for Chi distribution is mathematically given by

The test statistic is


X^2 = ((n-1)*s^2)/(\sigma^2)


X^2={70*0.32}{0.18}


X^2= 124.4

Since

Critical Value


C_(\alpha, df)=C_(0.99 , 70)


C_(0.99 , 70) =100.4252

Hence, we Reject
H_0 ,Given that 124.4 is Greater than 100.4252

Therefore

All the engine fan blades must be replaced

User TMBT
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