2. The article \"Study on the life Distribution of Microdrills\" (Z. Yang, Y. Ch

Question

2. The article "Study on the life Distribution of Microdrills" (Z. Yang, Y. Chen, and Y. Yang, Journal of Engineering Manufacture, 2002:301-305) reports that in a sample of 50 microdrills drilling a low-carbon alloy steel, the average lifetime (expressed as the number of holes drilled before failure) was 12.68 with a standard deviation of 6.83. Assume that the life time of the microdrills follows normal distribution with unknown mean (A) Find a 95% confidence interval for mean lifetime of microdrills under these conditions. (8 points) (B) An engineer reported a confidence interval of (11.09, 14.27) but neglected to specify the level of confidence. What is the level of this confidence interval? (7 points)

Explanation / Answer

Ans:

As,sample size,n>30,we can use z multiplier.

z value for 95% CI is 1.96

95% Confidenece interval for mean

=12.68+/-1.96*6.83/sqrt(50)

=12.68+/-1.89

=(10.79, 14.57)

b)Confidence interval with limits (11.09,14.27) is with 90% level of confidence.

when z=1.645 i.e 90% CI is used

90% Confidenece interval for mean

=12.68+/-1.645*6.83/sqrt(50)

=12.68+/-1.59

=(11.09, 14.27)

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