A mayor running for re-election claims that during his term, average municipal taxes have fallen by $175. A conscientious statistician wants to test this claim. He surveys 35 of his neighbors and finds that their taxes decreased (in dollars) as follows: 226, 200, 136, 219, 178, 230, 143, 224, 97, 114, 148, 282, 253, 205, 162, 169, 214, 113, 185, 301, 175, 129, 169, 138, 194, 126, 243, 155, 170, 201, 184, 168, 182, 150, 276 The statistician assumes a population standard deviation of $41. Do you think the statistician should reject the mayor's claim? Why or why not? Step 1: State the hypothesis. 1: Step 2: Determine the Features of the Distribution of Point Estimates Using the Central Limit Theorem. By the Central Limit Theorem, we know that the point estimates are with distribution mean :] and distribution standard deviation Step 3: Assuming the Claim is True, Find the Probability of Obtaining the Point Estimate. P(--:l> =P(--l:l> = Step 4: Make a Conclusion About the Claim. What do you think? Based on the probability you calculated in step 3 of obtaining the point estimate, would you reject the claim? Think about your answer to this step yourself; this step is not graded