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 38 of his neighbors and finds that their taxes decreased (in dollars) as follows:113, 85, 109, 97, 117, 87, 105, 116, 84, 122, 118, 107, 108, 115, 100, 100, 107, 111, 101, 108, 71, 107, 80, 103, 86, 121, 117, 83, 113, 107, 124, 102, 78, 112, 96, 97, 88, 117The statistician assumes a population standard deviation of $14. 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 ___ with distribution mean ____ and distribution standard deviation ______.Step 3: Assuming the Claim is True, Find the Probability of Obtaining the Point Estimate.P(___ ___ ___ ) = P(___ ___ _____ )= _____ **Title: Evaluating a Claim Using Statistical Methods**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 38 of his neighbors and finds that their taxes decreased (in dollars) as follows:113, 85, 109, 97, 117, 87, 105, 116, 84, 122, 118, 107, 108, 115, 100, 100, 107, 111, 101, 108, 71, 107, 80, 103, 86, 121, 117, 83, 113, 107, 124, 102, 78, 112, 96, 97, 88, 117The statistician assumes a population standard deviation of $14. Do you think the statistician should reject the mayor's claim? Why or why not?**Step 1: State the Hypothesis.**\[ \mu = \]**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.**\[ P(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_) = P(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_) = \]\[\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\]

A statistical hypothesis is an assumption or a statement about the population parameter. Hypothesis…

Answered: A mayor running for re-election claims…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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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 38 of his neighbors and finds that their taxes decreased (in dollars) as follows:

113, 85, 109, 97, 117, 87, 105, 116, 84, 122, 118, 107, 108, 115, 100, 100, 107, 111, 101, 108, 71, 107, 80, 103, 86, 121, 117, 83, 113, 107, 124, 102, 78, 112, 96, 97, 88, 117

The statistician assumes a population standard deviation of $14. 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 ___ with distribution mean ____ and distribution standard deviation ______.

Step 3: Assuming the Claim is True, Find the Probability of Obtaining the Point Estimate.

P(___ ___ ___ ) = P(___ ___ _____ )= _____

**Title: Evaluating a Claim Using Statistical Methods**

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 38 of his neighbors and finds that their taxes decreased (in dollars) as follows:

113, 85, 109, 97, 117, 87, 105, 116, 84, 122, 118, 107, 108, 115, 100, 100, 107, 111, 101, 108, 71, 107, 80, 103, 86, 121, 117, 83, 113, 107, 124, 102, 78, 112, 96, 97, 88, 117

The statistician assumes a population standard deviation of $14. Do you think the statistician should reject the mayor's claim? Why or why not?

**Step 1: State the Hypothesis.**

\[ \mu = \]

**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.**

\[ P(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_) = P(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_) = \]
\[
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
\]

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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