A mayor running for re-election claims that during his term, average municipal taxes have fallen by $225. A conscientious statistician wants to test this claim. She surveys 38 of her neighbors and finds that their taxes decreased (in dollars) as follows: 215, 219, 222, 218, 231, 226, 251, 219, 231, 233, 240, 234, 224, 224, 219, 235, 215, 225, 254, 254, 231, 217, 220, 231, 232, 193, 215, 224, 234, 220, 245, 236, 225, 186, 253, 212, 222, 221 The statistician assumes a population standard deviation of $16. Do you think the statistician should reject the mayor's claim? Why or why not? Step 1: State the hypothesis. 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 normally distributed v oo with distribution mean and distribution standard deviation Step 3: Assuming the Claim is True, Find the Probability of Obtaining the Point Estimate. P(x v P(z o 2 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.
A mayor running for re-election claims that during his term, average municipal taxes have fallen by $225. A conscientious statistician wants to test this claim. She surveys 38 of her neighbors and finds that their taxes decreased (in dollars) as follows: 215, 219, 222, 218, 231, 226, 251, 219, 231, 233, 240, 234, 224, 224, 219, 235, 215, 225, 254, 254, 231, 217, 220, 231, 232, 193, 215, 224, 234, 220, 245, 236, 225, 186, 253, 212, 222, 221 The statistician assumes a population standard deviation of $16. Do you think the statistician should reject the mayor's claim? Why or why not? Step 1: State the hypothesis. 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 normally distributed v oo with distribution mean and distribution standard deviation Step 3: Assuming the Claim is True, Find the Probability of Obtaining the Point Estimate. P(x v P(z o 2 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.
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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Transcribed Image Text:A mayor running for re-election claims that during his term, average municipal taxes have fallen by $225. A
conscientious statistician wants to test this claim. She surveys 38 of her neighbors and finds that their taxes
decreased (in dollars) as follows:
215, 219, 222, 218, 231, 226, 251, 219, 231, 233, 240, 234, 224, 224, 219, 235, 215, 225, 254, 254, 231,
217, 220, 231, 232, 193, 215, 224, 234, 220, 245, 236, 225, 186, 253, 212, 222, 221
The statistician assumes a population standard deviation of $16. Do you think the statistician should reject
the mayor's claim? Why or why not?
Step 1: State the hypothesis.
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 normally distributed v
os with
distribution mean
and distribution standard deviation
Step 3: Assuming the Claim is True, Find the Probability of Obtaining the Point Estimate.
P(x
svX o 2
P(z 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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