Testing for Variance : The fan blades on commercial jet engines must be replaced
ID: 3430070 • Letter: T
Question
Testing for Variance: The fan blades on commercial jet engines must be replaced when wear on these parts indicates too much variability to pass inspection. A large engine contains thousands of fan blades, and safety regulation requires that variability measurements on the population of all blades not exceed 0.18 mm2. An engine inspector took a random sample of 61 fans blades from an engine with a sample variance 0.27 mm2. Using a 0.05 level of significance, is the inspector justified in claiming that all the engine fan blades must be replaced?
For ?=0.05, find the confidence interval for the population variance. First state the upper and lower chi squared statistics accurate to two decimals.Round to the nearest hundredth:
?2L=
?2U=
Then give the lower and upper confidence intervals accurate to three decimals.
Lower Limit:
Upper Limit:
Explanation / Answer
Testing for Variance: The fan blades on commercial jet engines must be replaced when wear on these parts indicates too much variability to pass inspection. A large engine contains thousands of fan blades, and safety regulation requires that variability measurements on the population of all blades not exceed 0.18 mm2. An engine inspector took a random sample of 61 fans blades from an engine with a sample variance 0.27 mm2. Using a 0.05 level of significance, is the inspector justified in claiming that all the engine fan blades must be replaced?
For ?=0.05, find the confidence interval for the population variance. First state the upper and lower chi squared statistics accurate to two decimals.Round to the nearest hundredth:
?2L= 40.48
?2U= 83.30
Lower limit = (n-1) s2 / chisquare = 60*0.27/83.30=0.194
upperr limit = (n-1) s2 / chisquare = 60*0.27/40.48=0.400
Then give the lower and upper confidence intervals accurate to three decimals.
Lower Limit: 0.194
Upper Limit: 0.400
Population variance =0.18 not fall in the interval.
Reject the null hypothesis.
At 0.05 level of significance, the inspector justified in claiming that all the engine fan blades must be replaced.