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WISE-International Master

Hypothesis Testing

A hypothesis is a claim (conjecture/assumption) about a population parameter:

population mean population proportion It is always about a population parameter, not a sample statistic

A Common Theme

Check the merits of this hypothesis based on sample information sample A hypothesis is formed about some population parameter

infer

Hypothesis testing provides a general framework for approaching such inference problems

ˆ

The Null Hypothesis

Suppose that some hypothesis has been formed about the population parameter and that this hypothesis will be believed unless sufficient contrary evidence is produced.

This hypothesis can be thought of as a maintained hypothesis.

In the language of statistics, this hypothesis is called a null hypothesis, and is denoted as H0.

In hypothesis testing, the null hypothesis plays a role similar to that of a defendant on trial in many judicial systems. Just as a defendant is presumed to be innocent until proven guilty, the null hypothesis is presumed to be true until the data strongly suggest otherwise.

The Alternative Hypothesis, H1

Having a null hypothesis requires having an alternative hypothesis that challenges the null hypothesis.

In a Court of Law

H 0 : innocent H1 : guilty

The defendant is deemed innocent until the prosecution presents sufficiently strong contrary evidence to pronounce a verdict of guilty. Similarly, in hypothesis testing framework, the null hypothesis is initially held to be true unless the sample data persuade us to believe in favor of the alternative. i.e., we must have evidence “beyond reasonable doubt” against the null in order to conclude that the null is to be rejected.

Pairs of Hypotheses

H 0 : 0 H1 : 0 H 0 : 0 H1 :…...

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