Question

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?

Answer 1

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