ENGR 371: PROBABILITY AND STATISTICS
FOR ENGINEERS STUDY GUIDE FOR DEC
21 PREPARATION Concordia University
SESSION 4: Tests of Hypotheses for a Single Sample.
, Tests of Hypothesis for a Single Sample
Hypothesis Testing
A hypothesis is a statement about a population’s parameter. There are two types of hypothesis
• Null hypothesis (Ho): This always states that a population’s parameter is equal to some value.
• Alternative hypothesis (H1): This would state the parameter in the null hypothesis as an
inequality to the same value given in the null hypothesis.
Different outcomes may occur when testing the hypothesis. These outcomes are:
Decision Ho is true Ho is false
Reject Ho Type I error No error
Fail to reject Ho No error Type II error
The probability of each type of error is:
• α = P(type I error)
• β = P(type II error)
The β probability for a two sided hypothesis can be found by:
[ ] [ ]
δ √n δ √n
β=Φ z − −Φ −z −
α
2
σ α
2 σ
For an upper sided hypothesis:
[
β=Φ zα − δ √n
σ ]
For a lower sided hypothesis:
β=1−Φ −z α[ − δ √n
σ ]
Note that:
δ =μ−μ o
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