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MSOR221
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Topic Three
Inferences about a Population: Hypothesis Testing
Hypothesis testing
is a procedure based on sample evidence and probability theory to
determine whether the hypothesis is a reasonable statement and should not be rejected,
or is unreasonable and should be rejected.
The Classical Approach to Hypothesis Testing
1.
Formulate the null and alternative hypothesis.
2.
Decide on the level of significance.
3.
Determine the appropriate test statistic (or probability distribution).
4.
Find the critical value(s) and then establish the decision rule.
5.
Compute the value of the test statistic from sample information and make the
statistical decision.
6.
State the conclusion in words (or in the language of the problem).
1. Formulate the Null and Alternative Hypotheses

The null hypothesis
H
0
is the hypothesis that is always tested.

The alternative hypothesis
H
1
is set up as the opposite of the null hypothesis and
represents the conclusion supported if the null hypothesis is rejected.
Inequality Sign
Null Hypothesis
H
0
=
≥
≤
Alternative Hypothesis
H
1
≠
<
>
•
The statement of the null hypothesis always contains an equal sign regarding
the specified value of the parameter.
•
The statement of the alternative hypothesis never contains an equal sign
regarding the specified value of the parameter.
–
The null hypothesis always refers to a specified value of the population
parameter, not a sample statistic.
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2. Decide on the Level of Significance

The significance level,
α
, of a hypothesis test is defined as the probability of
making a Type
I
error, that is, the probability of rejecting a true null hypothesis.
–
In hypothesis testing four outcomes are possible, two of which lead to incorrect
decisions.
Actual Situation
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 Spring '09
 patrickchu

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