## The Research and Development department of a paint company has developed an additive that it hopes will increase the ability of the company’s stain for outdoor decks to resist water absorption.

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1. The Research and Development department of a paint company has developed an additive that it hopes will increase the ability of the company’s stain for outdoor decks to resist water absorption. The current formulation of the stain has a mean absorption rate of 35 units. Before changing the stain, a study was designed to evaluate whether the mean absorption rate of the stain with the additive was decreased from the current rate of 35 units.

a) State the appropriate null and alternative hypotheses. The null Hypothesis – H0: The true mean water absorption rate of the new additive is greater than or equal to 35 units. The Alternate Hypothesis – Ha- The true mean water absorption rate of the new additive is less than 35 units.

b) Describe type I and type II errors in the context of the problem. A type 1 error is the rejection of a true null hypothesis based on the result of a test, in the context of this problem that would mean that based on a test the true mean water absorption rate of the new additive is less than or equal to 35 units, yet in reality when it rains the water absorbed is continually greater than 35 units. A type 2 error is the failure to reject a false null hypothesis based on the result of a test, in the context of this problem that would mean that based on the results of a test you conclude that there is no change in water absorption or it is greater than 35 units, yet in reality when it rains the water absorbed continually is less than 35 units

Which of these errors do you consider to be more serious? Explain I consider a type 1 error in this situation to be more serious, this is due to the fact that a false positive would lead the company to believe their product is effective when in reality it is not. This could cause the company to produce, advertise, and sell an ineffective product which could have dire consequences.

c) The stain with the additive was applied to 50 pieces of decking material. As a result, � = 32.6 and � = 9.2. Based on the level of significance you chose in (b), state the conclusion in the context of the problem.