A jet engine turbine blade has holes that are specified as being 0.60 mm in diam

Question

A jet engine turbine blade has holes that are specified as being 0.60 mm in diameter. One blade with 15 holes is selected to evaluate the accuracy of the laser drilling process that is being used. The mean diameter of the 15 holes that are measured is 0.58 mm and the standard deviation of the process () is 0.009 mm 2) Calculate a 99% two-sided confidence interval for mean hole diameter, . Based on your answer to part (a), do you believe that the process is producing holes with a mean diameter of 0.60 mm? Explain your answer using information from part (a) a) b)

Explanation / Answer

Question 2

Part a

Here, we have to calculate the two sided 99% confidence interval for mean hole diameter.

We are given

Sample size = n = 15

Sample mean = Xbar = 0.58

Population mean = µ = 0.60

Population standard deviation = = 0.009

Confidence level = 99%

The confidence interval formula is given as below:

Confidence interval = Xbar -/+ Z*/sqrt(n)

Where Z is the critical value

For 99% confidence level, Z = 2.5758 (by using z-table)

Confidence interval = 0.58 -/+ 2.5758*0.009/sqrt(15)

Lower limit = 0.58 - 2.5758*0.009/sqrt(15)

Lower limit = 0.57401438

Upper limit = 0.58 + 2.5758*0.009/sqrt(15)

Upper limit = 0.58598562

Confidence interval = (0.57401438, 0.58598562)

Part b

Based on above answer, we do not believe that the process is producing holes with a mean of 0.60 mm because the process mean of 0.60 mm do not includes in the above confidence interval (0.57401438, 0.58598562).

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