Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A pea plant heterozygous for seed shape (round over wrinkled ) and seed colour (yellow over green ) is selfed. Among 320 offspring the numbers are: round yellow 191, round green 55, wrinkled yellow 52, wrinkled green 22. The null hypothesis is the ratio . At the level the critical value of chi-square is with degrees of freedom and with degree of freedom.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. Expected numbers first, then the sum of .
(a) . The other expected numbers are , and .
(b) . This is below , so the data fit .
(c) Four classes, one fixed total: degrees of freedom.
(d) Round is and wrinkled is . Expected are and . So with degree of freedom. It is below .
(e) For the two-by-two table of shape against colour, the expected cell numbers come from the row and column totals. The result is with degree of freedom, below , so there is no sign that the two genes are linked.
Check. The shortcut for the two-by-two table gives the same , and the exact fractions agree with the rounded values shown.
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