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# The Chi-Square Distribution and the Analysis of Frequencies (1).docx

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School
Department
Statistics
Course
STATS 2B03
Professor
Aaron Childs
Semester
Fall

Description
November 2 , 2012 Stats 2B03: Statistical Methods for Science The Chi-Square Distribution and the Analysis of Frequencies (1) - see Figure 9 in the courseware. There should be a similar amount of vertical variation for each of the four samples 12.3 Goodness of fit tests - example: Mendell bred green and yellow peas  g,g: pure green peas + y,y: pure yellow peas  cross fertilized then to get (according to his theory): g,y  his theory was that the ywllow gene (y) is dominant over the green gene (g). he took 8023 of these g,y peas and cross-fertilized them  g,y + g,y: g,g; g,y; y,g; y,y  according to his theory P = P(yellow pea) = ¾, P = P(green pea) = ¼ 1 2  he observed 6022 yellow peas and 2001 green peas. Are these frequencies consistent with Mendel’s theory?  In general we want to test whether an observed distribution of frequencies is consistent with some hypothesized distribution  H 0 the hypothesized distribution is correct  H A it is not correct  In our example we want to test H : 0 = 1, P = ¼2 H : PA¾, 1≠≠ ¼ 2 Table of observed frequencies Observed frequencies (O)
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