# Hypothesis Testing

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Hypothesis Testing: One Population

Hypothesis testing is used to make decisions about a population based on the analysis of sample statistics. There are always two hypothesis statements which are mutually exclusive and complementary statements concerning the value of the population parameter of interest:

Null Hypothesis (H0):

An assumption regarding a population parameter of interest. This hypothesis always includes the equal sign as the null hypothesis is assumed to be true unless sample data produces evidence to the contrary.

Alternative Hypothesis (H1):

The alternative option available when the null hypothesis is rejected.

Three Types of Hypothesis Tests:

Lower-Tail Test Upper-Tail Test Two-Tailed Test

H0: ( ( (0 H0: ( ( (0 H0: ( = (0
H1: ( < (0 H1: ( > (0 H1: ( ( (0

Two-Sided Tests:

A Two-Tailed Test (TTT) is designed to detect a change in the population parameter of interest from some hypothesized value to some different value.

One-Sided Tests:

A Lower-Tail Test (LTT) is designed to detect a change in the population parameter of interest from some hypothesized value to some lower value.

An Upper-Tail Test (UTT) is designed to detect a change in the population parameter of interest from some hypothesized value to some greater value.

Test Statistics and Action Limits:

A test statistic is a sample statistic corresponding to the population parameter being tested. For example, when testing a hypothesis for a population mean, the corresponding test statistic (not standardized) is the sample mean. For any hypothesis test the general form of the standardized test statistic is given by:

Sample Statistic - Hypothesized Value Standard Deviation of Sample Statistic

The rationale is that assuming the null hypothesis is true, the sample statistic should be reasonably...

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