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?
A complete, neat and step-by-step solution with explanation for testing the claim of the customers and of management, where the error is and why.