Question

A.) 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 ?² = 0.18 mm². An engine inspector took a random sample of 81 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?

Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)

What are the degrees of freedom?

Find a 90% confidence interval for the population standard deviation. (Round your answers to two decimal places.)

lower limit      mm                 upper limit   mm

B.) Jim Mead is a veterinarian who visits a Vermont farm to examine prize bulls. In order to examine a bull, Jim first gives the animal a tranquilizer shot. The effect of the shot is supposed to last an average of 65 minutes, and it usually does. However, Jim sometimes gets chased out of the pasture by a bull that recovers too soon, and other times he becomes worried about prize bulls that take too long to recover. By reading journals, Jim has found that the tranquilizer should have a mean duration time of 65 minutes, with a standard deviation of 15 minutes. A random sample of 7 of Jim's bulls had a mean tranquilized duration time of close to 65 minutes but a standard deviation of 26 minutes. At the 1% level of significance, is Jim justified in the claim that the variance is larger than that stated in his journal? Find a 95% confidence interval for the population standard deviation.

Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)

What are the degrees of freedom?

Find the requested confidence interval for the population standard deviation. (Round your answers to two decimal place.)

lower limit      mm                 upper limit   mm

Answer 1

A)

Null Hypothesis

Alternative Hypothesis

Under null hypothesis , the test statistic is

Degrees of freedom = n-1= 81-1 =80

The P-Value is 2.3X 10^-5

Since p value is less than significance level. REject H0.

Conclusion : At 1% level of significance there is sufficient evidence to conclude that the variance of measurements for the fan blades is higher than the specified amount.The inspectoe is justified in claiming that the blades must be replaced.

90% CI for population stanadard deviation :

Significance Level

The critical values of Chi square are

Answer: Lower limit = 0.50

Upper limit = 0.65