What Is Wrong with the Following "Proof" That −3 = $( - 3 ) ^ { 2 } = 3 ^ { 2 } \text {, or } 9 = 9 \text {. Therefore } - 3 = 3 \text {. }$

question 24

Essay

What is wrong with the following "proof" that −3 = 3, using backward reasoning? Assume that −3 = 3. Squaring both sides yields $( - 3 ) ^ { 2 } = 3 ^ { 2 } \text {, or } 9 = 9 \text {. Therefore } - 3 = 3 \text {. }$

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Definitions:

Confidence

In statistics, this refers to the degree to which one can be sure about the reliability of a statistical estimate, often expressed as a confidence interval.

F-distribution

A probability distribution that arises frequently as the null distribution of a test statistic, especially in analysis of variance.

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A type of insurance coverage specifically designed to provide protection against risks associated with owning and operating a motorcycle.

Significance Level

The threshold at which the results of statistical analysis are considered significant, typically set before the data is collected.