When two heterozygotes are mated, the ratios of the offspring produced should be in a 1:2:1 ratio if normal Mendelian segregation is occurring. If one of the alleles is dominant, then the phenotypes observed should be present in a 3:1 ratio with the dominant phenotype more common than the recessive one. We can use an ?² goodness-of-fit test to test whether the ratio of offspring is indeed 3:1. Imagine a cross is performed and the number of offspring observed are 67 with the dominant phenotype and 33 with the recessive phenotype. Using the table of critical values shown, what is the P-value range we would obtain for our test?
?
$\begin{array}{c}\chi^{2} \text { critical values }\\\text { for } d f=2\\\begin{array}{ll}\text { Sig. level } & \text { Value } \\\hline 0.05 & 3.84 \\0.025 & 5.02 \\0.01 & 6.63\end{array}\end{array}$

Question

When two heterozygotes are mated, the ratios of the offspring produced should be in a 1:2:1 ratio if normal Mendelian segregation is occurring. If one of the alleles is dominant, then the phenotypes observed should be present in a 3:1 ratio with the dominant phenotype more common than the recessive one. We can use an ?² goodness-of-fit test to test whether the ratio of offspring is indeed 3:1. Imagine a cross is performed and the number of offspring observed are 67 with the dominant phenotype and 33 with the recessive phenotype. Using the table of critical values shown, what is the P-value range we would obtain for our test?
?

\begin{array}{c}\chi^{2} \text { critical values }\\\text { for } d f=2\\\begin{array}{ll}\text { Sig. level } & \text { Value } \\\hline 0.05 & 3.84 \\0.025 & 5.02 \\0.01 & 6.63\end{array}\end{array}

Quizplus · Accepted Answer

The chi-square test is used to determine if there is a significant difference between the expected and observed frequencies. In this scenario, the expected ratio is 3:1 for dominant to recessive phenotypes. With 100 offspring, we would expect 75 with the dominant phenotype and 25 with the recessive phenotype. The chi-square statistic is calculated as follows: $\chi^2 = \frac{(67-75)^2}{75} + \frac{(33-25)^2}{25} = \frac{64}{75} + \frac{64}{25} = 0.853 + 2.56 = 3.413$. This value is less than the critical value of 3.84 for a significance level of 0.05, indicating that the difference between observed and expected frequencies is not statistically significant, and thus, the P-value is greater than 0.05.

When Two Heterozygotes Are Mated, the Ratios of the Offspring