The rationale behind the one-sample chi-square or goodness-of-fit test is that for any set of occurrences, you can easily compute what you would expect by chance. You do this by dividing the total number of occurrences by the number of classes or categories. In this example using data from the Census, the observed total number of occurrences is 84. We would expect that, by chance, 84/3 (84, which is the total of all frequencies, divided by 3, which is the total number of categories), or 28, respondents would fall into each of the three categories of level of education. Then we look at how
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