In tomato plants, two genes control fruit color and leaf shape:

For fruit color, the allele for red fruit ( $R$ ) is dominant to the allele for yellow fruit ( $r$ ).
For leaf shape, the allele for cut leaf ( $C$ ) is dominant to the allele for potato leaf ( $c$ ).

A geneticist crossed two tomato plants that were heterozygous for both genes ( $R r C c$ ). The expected phenotypic ratio of their offspring is $9 : 3 : 3 : 1$ .

The geneticist obtained 160 offspring from this cross. The observed numbers for each phenotype were:

Red fruit, cut leaf: 81
Yellow fruit, cut leaf: 36
Red fruit, potato leaf: 33
Yellow fruit, potato leaf: 10

Use the chi-squared formula

\chi^2 = \sum \frac{(O - E)^2}{E}

to calculate the $\chi^2\,$ value for these data.

State the number of degrees of freedom for this test.

Using the critical values table below (for $p = 0.05$ ), determine whether the null hypothesis (that there is no significant difference between the observed and expected results) should be accepted or rejected, and explain your answer.

Degrees of freedom	Critical value ( $p = 0.05$ )
1	3.84
2	5.99
3	7.82
4	9.49

In tomato plants, two genes control fruit color and leaf shape:

For fruit color, the allele for red fruit ( $R$ ) is dominant to the allele for yellow fruit ( $r$ ).
For leaf shape, the allele for cut leaf ( $C$ ) is dominant to the allele for potato leaf ( $c$ ).

A geneticist crossed two tomato plants that were heterozygous for both genes ( $R r C c$ ). The expected phenotypic ratio of their offspring is $9 : 3 : 3 : 1$ .

The geneticist obtained 160 offspring from this cross. The observed numbers for each phenotype were:

Red fruit, cut leaf: 81
Yellow fruit, cut leaf: 36
Red fruit, potato leaf: 33
Yellow fruit, potato leaf: 10

Use the chi-squared formula

\chi^2 = \sum \frac{(O - E)^2}{E}

to calculate the $\chi^2\,$ value for these data.

State the number of degrees of freedom for this test.

Degrees of freedom	Critical value ( $p = 0.05$ )
1	3.84
2	5.99
3	7.82
4	9.49

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