7. Product and Process Comparisons 7.1. Introduction 7.1.5. What is the relationship between a test and a confidence interval? |
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There is a correspondence between hypothesis testing and confidence intervals |
In general, for every test of hypothesis there is an equivalent
statement about whether the hypothesized parameter value is
included in a confidence interval. For example, consider the
previous example of linewidths where
photomasks are tested to ensure that their linewidths have a mean
of 500 micrometers. The null and alternative hypotheses are:
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Hypothesis test for the mean |
For the test, the sample mean, |
Equivalent confidence interval |
With some algebra, it can be seen that the null hypothesis is
rejected if and only if the value 500 micrometers is not in the
confidence interval
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Equivalent confidence interval | In fact, all values bracketed by this interval would be accepted as null values for a given set of test data. |