Assume you are the manager of a paint manufacturing factory. Your company has re

Question

Assume you are the manager of a paint manufacturing factory.  Your company has received complaints from customers that the containers hold less than the amount printed on them.  On the other hand, corporate management is concerned that the containers hold more than the standard amount.  You assign a statistician to verify the claims by the customers and the corporate management.  A sample of containers was selected and the volume of paint in each container was measured.  Assuming that the volume printed on each container is 1 gallon, how would you formulate the null and alternative hypotheses to test the customers’ claim?  That of the corporate management?  Both customers and corporate management?  As a manager, what reasonable criteria will you use to set a value for the level of significance to be used in the test?  Suppose you arrive at the decision that there is not enough evidence to reject the null hypothesis, could you have made a mistake?  What type of error would result in that case?

Explanation / Answer

Null Hypothesis: There is no evidence thatcontainers hold less than the amount printed on them Alternative Hypothesis: There is an evidencethat containers hold less than the amount printed onthem We have to use t-test for this We assume 0.05 as a level ofsignificance If we reject the null hypothesis if we arriveat the decision that there is not enough evidence to reject thenull hypothesis, then this is a mistake and this mistake results asthe Type-I error

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