Hypothesis Testing Cheat Sheet by NatalieMoore

Draw conclu­sions from a set of data

The major question to answer is whether a difference between samples, or between a sample and a popula­tion, has occurred simply as a result of natural variation or because of a real difference between the two

The altern­ative hypothesis may be classified as two-tailed or one-tailed

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is a two-sided altern­ative

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the altern­ative hypothesis is written: H1: µ =/= µo

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one-sided altern­ative

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E.g. the altern­ative hypothesis is written as: H1: µ > µo

1.

Collecting the data

3.

Setting up a hypothesis (i.e. a claim or theory), which is to be tested

5.

Either accepting or rejecting the hypothesis

After the approp­riate hypotheses have been formul­ated, we must decide upon the signif­icance level (or α -level) of the test

A 5% signif­icance level says in effect that an event has occurred that occurs less than 5% of the time is considered unusual

Deals with the case of a single sample being chosen from a population and the question of whether that particular sample might be consistent with the rest of the population

Inform­ation required in calcul­ation

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the mean of the sample

Other inform­ation of interest might include:

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Is the popula­tion’s standard deviation known?

There are different cases for the one-sample z-test statistic

the population has a normal distri­bution and

the sample size, n, is large (i.e. at least 25), and

the population has any distri­bution

the value of population standard devation is unknown (however, since n is large, the value of population standard devation is approx­imated by the sample standard deviation, s)

Statement that nothing unusual has occurred

The notation is H1 or HA

Two possible errors in making a conclusion about a null hypothesis

Type II errors occur when you accept H0 (i.e. conclude that it is true) when H0 is really false.