a) The standard strength of steel wire is required to have a mean of 1250MPa. A new process is introduced in the product

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A The Standard Strength Of Steel Wire Is Required To Have A Mean Of 1250mpa A New Process Is Introduced In The Product 1 (72.68 KiB) Viewed 41 times

a) The standard strength of steel wire is required to have a mean of 1250MPa. A new process is introduced in the production of steel wire, and a random sample consisting of 25 measurements gives an average strength of 1312MPa and standard deviation, sMPa. It is assumed that the observation of steel wire strength is normally distributed. i. If the lower limit of 90% confidence interval for the true variability of the strength of steel wire made by a new process is 14436.2488, find the sample standard deviation of the strength of steel wire. (3 marks) ii. Hence, is there significant evidence that the mean strength is greater than the standard specification? Use α=0.01 level of significance. (5 marks) b) Mechanical components are being produced continuously. A quality control program for the mechanical components requires a close estimate of the defective proportion in production when all settings are correct for all machines. 110 components are examined from machine A under these conditions, and 22 of them are found to be defective. Another 1250 components are examined from machine B, also under the same conditions, and 1230 of them are found to be non-defective. Is there any evidence that machine B is better than machine A after the conditions are met? Test at α=0.05 level of significance. (7 marks)