## Question

###### An experiment was performed to compare the fracture toughness of high-purity 18 Ni maraging steel with...

An experiment was performed to compare the fracture toughness of high-purity 18 Ni maraging steel with commercial purity steel of the same type. For m = 34 specimens, the sample average toughness was x = 63.1 for the high-purity steel, whereas for n = 39 specimens of commercial steel y = 57.3. Because the high- purity steel is more expensive, its use for a certain application can be justified only if its fracture toughness exceeds that of commercial-purity steel by more than 5. Suppose that both toughness distributions are normal. (a) Assuming that 01 = 1.2 and 02 = 1.1, test the relevant hypotheses using a = 0.001 5:51 PM (b) Compute B for the test conducted in part (a) when u1 - 2 = 6. (Round your answer to four decimal places.) 5:51 PM

## Answers

b) This is a right tailed test.

We will fail to reject the null (commit a Type II error) if we get a Z statistic less than 3.0902.( using excel formula =-NORM.S.INV(0.001))

This 3.0902 Z-critical value corresponds to some X critical value, such that

So I will incorrectly fail to reject the null as long as a draw a sample mean that is lesser than 5.837. To complete the problem what I now need to do is compute the probability of drawing a sample mean lesser than 5.837 given . Thus, the probability of a Type II error is given by

( using excel formula=NORM.S.DIST(-0.6017,TRUE) )

We were unable to transcribe this imageWe were unable to transcribe this imageA B с D E F H J K 1 SD N Mean 63.1 х 1.2 34 2 a) 3 Y 57.3 1.1 39 4 5 2.9533 ((C2-C3)-5)/SQRT((D2^2/E2)+(D342/E3)) 6 0.001 7 .-NORM.S.INV(C6) Test statistic significance level ZT critical Rejection Region P value for right tailed test 8 3.0902 2>3.0902 0.0016 9 1-NORM.S.DIST(C5,TRUE) 10 11 12 13 Since the test statistic do not lie in the rejection region and P value is less than the significance level, we have no evidence to say that the difference between the mean fracture toughness is greater than 5. 14We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image

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