True or False: When testing a claim using a simple random sample of ten matched pairs of heights, hypothesis tests using the p-value method, critical value method and confidence interval method will all result in the same conclusion.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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**Practice Problems:**

**True or False:** When testing a claim using a simple random sample of ten matched pairs of heights, hypothesis tests using the p-value method, critical value method and confidence interval method will all result in the same conclusion.

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In this practice problem, students are asked to determine whether the statement is true or false. The problem involves understanding the consistency of conclusions derived from different statistical methods when testing a hypothesis. Specifically, it examines if the p-value method, critical value method, and confidence interval method lead to the same conclusion when analyzing a simple random sample of ten matched pairs of heights.

- **P-Value Method:** This method determines significance by comparing the p-value to a predetermined significance level (α). If the p-value is less than α, the null hypothesis is rejected.
- **Critical Value Method:** This involves comparing a test statistic to a critical value determined from a statistical distribution. If the test statistic exceeds the critical value, the null hypothesis is rejected.
- **Confidence Interval Method:** This method involves constructing a confidence interval around the sample statistic. If the interval does not contain the null hypothesis value, it is rejected.

These methods often lead to the same conclusion, especially when the same significance level is used, but students are encouraged to explore situations where methods might differ and understand the underlying assumptions and calculations of each. 

Note: There are no graphs or diagrams presented in the given text that require any additional explanation.
Transcribed Image Text:**Practice Problems:** **True or False:** When testing a claim using a simple random sample of ten matched pairs of heights, hypothesis tests using the p-value method, critical value method and confidence interval method will all result in the same conclusion. --- In this practice problem, students are asked to determine whether the statement is true or false. The problem involves understanding the consistency of conclusions derived from different statistical methods when testing a hypothesis. Specifically, it examines if the p-value method, critical value method, and confidence interval method lead to the same conclusion when analyzing a simple random sample of ten matched pairs of heights. - **P-Value Method:** This method determines significance by comparing the p-value to a predetermined significance level (α). If the p-value is less than α, the null hypothesis is rejected. - **Critical Value Method:** This involves comparing a test statistic to a critical value determined from a statistical distribution. If the test statistic exceeds the critical value, the null hypothesis is rejected. - **Confidence Interval Method:** This method involves constructing a confidence interval around the sample statistic. If the interval does not contain the null hypothesis value, it is rejected. These methods often lead to the same conclusion, especially when the same significance level is used, but students are encouraged to explore situations where methods might differ and understand the underlying assumptions and calculations of each. Note: There are no graphs or diagrams presented in the given text that require any additional explanation.
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