### Chapter 7. Hypothesis Testing: Introduction to Hypothesis Testing (Critical Region Approach

### Assumptions of the z-test

The following assumptions are required to hold in order for a #z#-test to produce valid conclusions:

**Random sampling**

The process of inferential statistics heavily relies on the assumption that the sample being analyzed is *representative* of the larger population it is drawn from. Random sampling helps ensure the representativeness of the sample.

**Independent observations**

Two observations are said to be independent when the occurrence of one observation does not influence the chances of the second observation occurring.

**The value of #\sigma# is unchanged by the treatment**

When testing for a treatment effect, it is assumed that the amount of variability in the treated population is equal to the amount of variability in the untreated population.

**Normal sampling distribution**

When conducting a #Z#-test the *Standard Normal Table *is used to determine the boundaries of the critical region. This table can only be used when the *central limit theorem *holds and the distribution of sample means is normal.

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