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Chapter 12: Hypothesis Tests – Large Samples
Definition: Type II Error
A Type II Error occurs if a null hypothesis which is false is not rejected.
To make an inference for the study, the statistical test and level of
significance are used. So when we reject or do not reject the null
hypothesis, how confident are we that we are making the correct decision?
This question can be answered by specifying the
level of significance
.
Definition: Level of Significance
The level of significance, denoted by the Greek letter α (read as alpha), is the
probability of a Type I error.
That is, it is the probability of rejecting a true null hypothesis.
Typical values for
are 0.01, 0.02, 0.05, and 0.1. For example, if
= 0.05
for a test, and the null hypothesis is rejected, then one will be 95 percent
confident that this is the correct decision.
Note:
We will not address the probability of a Type II error in the text
because of its complexity.
Once the level of significance is selected, a critical value for the appropriate
test is selected. Such values may be obtained from a table or by using the
appropriate technology. For example, if a
z
test is used, the critical value
may be obtained by using the
Inverse Normal Distribution
workbook.
Definition: Critical Value
A critical value separates the critical region from the non-critical region.
Next, we will define what we mean by a critical region.