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A mayor running for re-election claims that during his term, average municipal taxes have fallen by $125. A conscientious statistician wants to test this claim. She surveys 38 of her neighbors and finds that their taxes decreased (in dollars) as follows: 102, 129, 94, 182, 126, 146, 145, 154, 158, 142, 73, 198, 151, 115, 177, 136, 159, 89, 105, 145, 69, 154, 140, 107, 127, 172, 69, 158, 77, 82, 192, 116, 53, 134, 98, 97, 180, 146 The statistician assumes a population standard deviation of $36. Do you think the statistician should reject the mayor's claim? Why or why not?

A mayor running for re-election claims that during his term, average municipal taxes have fallen by $125. A conscientious statistician wants to test this claim. She surveys 38 of her neighbors and finds that their taxes decreased (in dollars) as follows: 102, 129, 94, 182, 126, 146, 145, 154, 158, 142, 73, 198, 151, 115, 177, 136, 159, 89, 105, 145, 69, 154, 140, 107, 127, 172, 69, 158, 77, 82, 192, 116, 53, 134, 98, 97, 180, 146 The statistician assumes a population standard deviation of $36. Do you think the statistician should reject the mayor's claim? Why or why not?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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A mayor running for re-election claims that during his term, average municipal taxes have fallen by $125. A conscientious statistician wants to test this claim. She surveys 38 of her neighbors and finds that their taxes decreased (in dollars) as follows: 102, 129, 94, 182, 126, 146, 145, 154, 158, 142, 73, 198, 151, 115, 177, 136, 159, 89, 105, 145, 69, 154, 140, 107, 127, 172, 69, 158, 77, 82, 192, 116, 53, 134, 98, 97, 180, 146 The statistician assumes a population standard deviation of $36. Do you think the statistician should reject the mayor's claim? Why or why not? Step 1: State the hypothesis. ? V %3D 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 Select an answer with distribution mean and distribution standard deviation Step 3: Assuming the Claim is True, Find the Probability of Obtaining the Point Estimate. P(? v? v = P( ? v ? v 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.
Transcribed Image Text:A mayor running for re-election claims that during his term, average municipal taxes have fallen by $125. A conscientious statistician wants to test this claim. She surveys 38 of her neighbors and finds that their taxes decreased (in dollars) as follows: 102, 129, 94, 182, 126, 146, 145, 154, 158, 142, 73, 198, 151, 115, 177, 136, 159, 89, 105, 145, 69, 154, 140, 107, 127, 172, 69, 158, 77, 82, 192, 116, 53, 134, 98, 97, 180, 146 The statistician assumes a population standard deviation of $36. Do you think the statistician should reject the mayor's claim? Why or why not? Step 1: State the hypothesis. ? V %3D 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 Select an answer with distribution mean and distribution standard deviation Step 3: Assuming the Claim is True, Find the Probability of Obtaining the Point Estimate. P(? v? v = P( ? v ? v 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.
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