Testing for Variance The fan blades on commercial jet engine

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:

Solution

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.