A mayor running for re-election claims that during his term, average municipal taxes have fallen by $100. A conscientious statistician wants to test this claim. He surveys 44 of his neighbors and finds that their taxes decreased (in dollars) as follows: 50, 0, 67, 52, 207, 161, 159, 150, 95, 145, 84, 102, 69, 136, 109, 58, 125, 149, 145, 179, 126, 83, 132, 173, 109, 100, 162, 46, 49, 114, 89, 12, 239, 35, 114, 92, 27, 102, 90, 123, 122, 159, 138, 138 The statistician assumes a population standard deviation of $48. Do you think the statistician should reject the mayor's claim? Why or why not? Step 1: State the hypothesis. Correct = Correct 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 Correct with distribution mean Incorrect100 and distribution standard deviation Incorrect7.2362722698663. Step 3: Assuming the Claim is True, Find the Probability of Obtaining the Point Estimate. P(P( )=P()=P( Correct )=)= 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?
A mayor running for re-election claims that during his term, average municipal taxes have fallen by $100. A conscientious statistician wants to test this claim. He surveys 44 of his neighbors and finds that their taxes decreased (in dollars) as follows:
50, 0, 67, 52, 207, 161, 159, 150, 95, 145, 84, 102, 69, 136, 109, 58, 125, 149, 145, 179, 126, 83, 132, 173, 109, 100, 162, 46, 49, 114, 89, 12, 239, 35, 114, 92, 27, 102, 90, 123, 122, 159, 138, 138
The statistician assumes a population standard deviation of $48. Do you think the statistician should reject the mayor's claim? Why or why not?
Step 1: State the hypothesis.
Correct = Correct
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 Correct with distribution mean Incorrect100 and distribution standard deviation Incorrect7.2362722698663.
Step 3: Assuming the Claim is True, Find the Probability of Obtaining the Point Estimate.
P(P( )=P()=P( Correct )=)=
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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