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

### Hypothesis Testing Procedure

This chapter introduces the concept of *hypothesis testing*, one of the most commonly used inferential procedures.

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Hypothesis Testing

**Hypothesis testing** is a statistical procedure that is used to draw inferences about a population on the basis of sample data. There are many different hypothesis tests and although they all have their own nuances, the general procedure is the same for each one:

- State the hypotheses
- Determine the criteria for a decision
- Collect data and compute the test statistic
- Make a decision

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To illustrate the concept of hypothesis testing, a #z#-test will be used to investigate an example research scenario.

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z-test

A #\boldsymbol{z}#-**test** uses sample data to test hypotheses about an unknown population mean #\mu#.

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1. Research Question

A university wants to determine the effectiveness of a new Summer Course aimed at improving the statistical knowledge of its students. The students are graded on a scale from #0# to #10#, and from previous years it is known that the population of students currently has a mean grade of #\mu=6.5# and a standard deviation of #\sigma=1#.

In order to test the impact of the Summer Course, a total of #n=100# students are randomly selected to participate in the Summer Course.

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