Determine whether the claim stated below represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that (a) rejects the null hypothesis or (b) fails to reject the null hypothesis? An automotive manufacturer claims that the standard deviation for the gas mileage of one of the vehicles it manufactures is less than 2.2 miles per gallon. Does the claim represent the null hypothesis or the alternative hypothesis? Since the claim does not contain a statement of equality, it represents the alternative hypothesis. (a) How should you interpret a decision that rejects the null hypothesis? There is sufficient evidence to support the claim that the standard deviation for the gas mileage of one of the vehicles it manufactures is less than 2.2 miles per gallon. (b) How should you interpret a decision that fails to reject the null hypothesis? There is v evidence to v the claim that the standard deviation for the gas mileage of one of the vehicles it manufactures is less than 2.2 miles
Determine whether the claim stated below represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that (a) rejects the null hypothesis or (b) fails to reject the null hypothesis? An automotive manufacturer claims that the standard deviation for the gas mileage of one of the vehicles it manufactures is less than 2.2 miles per gallon. Does the claim represent the null hypothesis or the alternative hypothesis? Since the claim does not contain a statement of equality, it represents the alternative hypothesis. (a) How should you interpret a decision that rejects the null hypothesis? There is sufficient evidence to support the claim that the standard deviation for the gas mileage of one of the vehicles it manufactures is less than 2.2 miles per gallon. (b) How should you interpret a decision that fails to reject the null hypothesis? There is v evidence to v the claim that the standard deviation for the gas mileage of one of the vehicles it manufactures is less than 2.2 miles
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:**Exploring Hypothesis Testing: A Practical Example**
In hypothesis testing, we often need to discern whether a given claim aligns with the null hypothesis or the alternative hypothesis. Evaluating this provides insights into making informed decisions in statistical analysis. Here's an example for better understanding:
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**Scenario:**
An automotive manufacturer asserts that the standard deviation for the gas mileage of one of its vehicles is less than 2.2 miles per gallon.
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**Key Question:**
Does this claim represent the null hypothesis or the alternative hypothesis?
**Analysis:**
- Since the claim *does not contain* a statement of equality, it represents the **alternative hypothesis**.
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**Decision Interpretation:**
**(a) Interpretation if the Null Hypothesis is Rejected:**
- There is **sufficient evidence to support** the claim that the standard deviation for the gas mileage of one of the vehicles it manufactures is less than 2.2 miles per gallon.
**(b) Interpretation if the Null Hypothesis is Not Rejected:**
- There is ___ evidence to ___ the claim that the standard deviation for the gas mileage of one of the vehicles it manufactures is less than 2.2 miles per gallon.
(Note: The blanks suggest the need to fill in the conclusion based on the test results.)
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This exercise illustrates the importance of distinguishing between hypotheses and how decisions are made to validate a claim statistically. By identifying the hypothesis type, we better understand the implications of statistical testing in real-world contexts.
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