7. Hypothesis Testing: Introduction to Hypothesis Testing
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
- Set the criteria for a decision
- Collect the sample data and compute the test statistic
- Calculate the critical value and/or the #p#-value
- 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. Example: 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.
