Problem 1A manufacturer uses two machines to drill holes in pieces of sheet metal used in engineconstruction. The workers who attach the sheet metal to the engine become inspectors in thatthey reject sheets so poorly drilled that they cannot be attached. The production manager isinterested in knowing whether one machine produces more defective drillings than the othermachine. As an experiment, employees mark the sheets so that the manager can determinewhich machine was used to drill the holes. A random sample of 191 sheets of metal drilled bymachine 1 is taken, and 38 of the sheets are defective. A random sample of 202 sheets of metaldrilled by machine 2 is taken, and 21 are defective. Use ? = 0.05 to determine whether theproportion of sheets drilled with defective holes is significantly larger for machine 1.Use the ?-value approach. A manufacturer uses two machines to drill holes in pieces of sheet metal used in engine construction. The workers who attach the sheet metal to the engine become inspectors in that they reject sheets so poorly drilled that they cannot be attached. The production manager is interested in knowing whether one machine produces more defective drillings than the other machine. As an experiment, employees mark the sheets so that the manager can determine which machine was used to drill the holes. A random sample of 191 sheets of metal drilled by machine 1 is taken, and 38 of the sheets are defective. A random sample of 202 sheets of metal drilled by machine 2 is taken, and 21 are defective. Use α = 0.05 to determine whether the proportion of sheets drilled with defective holes is significantly larger for machine 1. Use the p-value approach.

Null and alternative hypothesis: Significance level: α=0.05 The sample proportions are,The pooled proportion or weighted estimate of p is, The value of Test statistic is,The P-value of the hypothesis test is, Since the p-value is less than the level of significance, so we reject the null hypothesis at specified significance level. Conclusion: There is sufficient evidence to support the claim that the proportion of sheets drilled with defective holes is significantly larger for machine 1.

Answered: A manufacturer uses two machines to…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Problem 1
A manufacturer uses two machines to drill holes in pieces of sheet metal used in engine
construction. The workers who attach the sheet metal to the engine become inspectors in that
they reject sheets so poorly drilled that they cannot be attached. The production manager is
interested in knowing whether one machine produces more defective drillings than the other
machine. As an experiment, employees mark the sheets so that the manager can determine
which machine was used to drill the holes. A random sample of 191 sheets of metal drilled by
machine 1 is taken, and 38 of the sheets are defective. A random sample of 202 sheets of metal
drilled by machine 2 is taken, and 21 are defective. Use ? = 0.05 to determine whether the
proportion of sheets drilled with defective holes is significantly larger for machine 1.
Use the ?-value approach.