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The following shows an example of the \chi ^2 method applied to experiments performed by the biologist Gregor Mendel (July 20, 1822 January 6, 1884).
In one of his famous experiments (sometimes called Mendel's First Experiment) he crossed strains of garden peas with yellow and green seeds. He then allowed the F_1 generation (which were all yellow) to self-fertilize, collected the resulting seeds and grew them all. In the resulting F_2 generation, he found that the ratio yellow:green was 3:1.

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The union of two sets A and B is the set containing all the elements of A and B.

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This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AQA A-Level (UK - Pre-2017)S4Goodness of fitXTRA-
Edexcel A-Level (UK - Pre-2017)S3Goodness of fitXTRA-
Edexcel AS Further Maths 2017Further Statistics 1ExtraGoodness of Fit - Extra-
Edexcel AS/A2 Further Maths 2017Further Statistics 1ExtraGoodness of Fit - Extra-
I.B. Higher Level7Goodness of fitXTRA-
OCR A-Level (UK - Pre-2017)S3Goodness of fitXTRA-
OCR AS Further Maths 2017StatisticsExtraGoodness of Fit - Extra-
OCR MEI AS Further Maths 2017Statistics AChi-Squared TestsGoodness of Fit - Extra-
OCR-MEI A-Level (UK - Pre-2017)S3Goodness of fitXTRA-
Universal (all site questions)GGoodness of fitXTRA-