# Stats: Hypothesis Testing

Definitions

- Null Hypothesis ( H
_{0} )
- Statement of zero or no change. If the original claim includes equality (<=, =, or >=), it is
the null hypothesis. If the original claim does not include equality (<, not equal, >) then the
null hypothesis is the complement of the original claim. The null hypothesis
*always*
includes the equal sign. The decision is based on the null hypothesis.
- Alternative Hypothesis ( H
_{1} or H_{a} )
- Statement which is true if the null hypothesis is false. The type of test (left, right, or
two-tail) is based on the alternative hypothesis.
- Type I error
- Rejecting the null hypothesis when it is true (saying false when true). Usually the more
serious error.
- Type II error
- Failing to reject the null hypothesis when it is false (saying true when false).
- alpha
- Probability of committing a Type I error.
- beta
- Probability of committing a Type II error.
- Test statistic
- Sample statistic used to decide whether to reject or fail to reject the null hypothesis.
- Critical region
- Set of all values which would cause us to reject H
_{0}
- Critical value(s)
- The value(s) which separate the critical region from the non-critical region. The critical
values are determined independently of the sample statistics.
- Significance level ( alpha )
- The probability of rejecting the null hypothesis when it is true. alpha = 0.05 and alpha =
0.01 are common. If no level of significance is given, use alpha = 0.05. The level of
significance is the complement of the level of confidence in estimation.
- Decision
- A statement based upon the null hypothesis. It is either "reject the null hypothesis" or
"fail to reject the null hypothesis". We will never accept the null hypothesis.
- Conclusion
- A statement which indicates the level of evidence (sufficient or insufficient), at what
level of significance, and whether the original claim is rejected (null) or supported
(alternative).

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