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Problem 2. You are a hydrologist who is reviewing a drainage plan for a new subdivision. According to the proposed plan, drainage is adequate if average annual rainfall is less than 35 inches. As an ethical engineer, you will only approve the plan if you certain that the drainage will be adequate, with signicance 0.05. The annual rainfall meausurements from the last ve years are: 34.2 23.4 33.7 38.2 32.8 Answer the following questions assuming that annual rainfall is normally distributed. (a) What are the null and alternative hypotheses? What is the signicance level? (b) Do you approve the drainage plan? (c) What is the probability of a Type I error? Without using any equations or statistical jargon, explain what a Type I error is for this situation. (d) What is the probability of a Type II error if the true average annual rainfall is 34 inches? Without using any equations or statistical jargon, explain what a Type 11 error is for this situation. (For this part and the next, assume that the 5 found in the above sample is actually the true value of 0') (c) How many years of data would we need to reduce the Type 11 error probability in part (d) to less than 0.10