Question

A researcher crossed several randomly-chosen pink tree peonies, Paeonia suffruticosa, to test a genetic model of inheritance. She expected to see red:pink:white offspring colors in the ratio of 12:3:1. Below are the observed color proportions of the 83 plants in the study: Observed Proportions of Progeny Colors Red Pink White 0.747, 0.205, 0.048, Conduct a hypothesis test to determine if the observed proportions significantly differ from the expected ratio. Given: critical = 5.99

Answer 1

Solution:

The null and alternative hypotheses are:

The observed proportions do not significantly differ from the expected ratio.

The observed proportions significantly differ from the expected ratio.

Under the null hypothesis, the test statistic is:

Where:

O is the observed frequencies

E is the expected frequencies.

Conclusion: Since the chi-square test statistic is less than the chi-square critical value 5.99, we, therefore, fail to reject the null hypothesis and conclude that the observed proportions do not significantly differ from the expected ratio.

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