STA 2023 Lecture Notes - Lecture 45: Frequency Distribution, Analysis Of Variance
Chapter 11
Chi-Square and Analysis of Variance (ANOVA)
Section 11.1 Test for Goodness of Fit
The chi-square statistic can be used to see whether a frequency distribution fits a
specific pattern. This is referred to as the chi-square goodness-of-fit test.
Formula for the test for goodness of fit:
where
d.f= number of categories minus 1
O- observed frequency
E= expected frequency
Assumption of Goodness of Fit
1. The data are obtained from a random sample
2. The expected frequency for each category must be 5 or more.
Example 1:
Students who are home-schooled often attend their local school as to participate in
various type of activities such as sports or musical ensembles. According to the
government, 82% of home-schoolers received their education entirely at home;
while 12% attend school up to 9 hours per week and 6% spend from 9 to 25 hours
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Document Summary
The chi-square statistic can be used to see whether a frequency distribution fits a specific pattern. This is referred to as the chi-square goodness-of-fit test. Formula for the test for goodness of fit: where d. f= number of categories minus 1. Assumption of goodness of fit: the data are obtained from a random sample, the expected frequency for each category must be 5 or more. Students who are home-schooled often attend their local school as to participate in various type of activities such as sports or musical ensembles. According to the government, 82% of home-schoolers received their education entirely at home; while 12% attend school up to 9 hours per week and 6% spend from 9 to 25 hours per week at school. A survey of 85 students who are home-schooled revealed the following information about where they received their education. Step 1 state the hypotheses and identify the claim. Ho: the proportions match those stated by the government.
