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APBIO141-031 with labs S14 - CollegeBoard* AP Exam Prep: Chi-squared Practice

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In a strain of tomato plants, short plant height and small fruit size are traits that display autosomal recessive patterns of inheritance. To investigate whether the traits segregate independently, researchers cross a pure-breeding line of tall tomato plants that have large fruits with a pure-breeding line of short tomato plants that have small fruits. The researchers observe that all the plants in the F1 generation are tall and have large fruits. The researchers cross the F1 plants with one another to generate an F2 generation. The researchers record observations for the F2 generation and will use the data to perform a chi-square goodness-of-fit test for a model of independent assortment. The setup for the chi-square goodness-of-fit test is shown in Table 1. Table 1. Observed and expected counts of tomato plants in the F2 generation Phenotype Observed Expected Tall plant with large fruits 104 90 Tall plants with small fruits 17 30 Short plant with large fruits 26 30 Short plant with small fruits 13 10 The researchers choose a significance level of p=0.05. Which of the following best completes the chi-square goodness-of-fit test?

Options
A.The calculated chi-square value is 9.24, and the critical value is 7.82. The null hypothesis of independent assortment can be rejected.
B.The calculated chi-square value is 13.13, and the critical value is 9.49. The null hypothesis of independent assortment cannot be rejected.
C.The calculated chi-square value is 9.24, and the critical value is 9.49. The null hypothesis of independent assortment cannot be rejected.
D.The calculated chi-square value is 13.13, and the critical value is 7.82. The null hypothesis of independent assortment can be rejected.
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Step-by-Step Analysis
First, let's restate the problem setup to ensure clarity: we have a dihybrid cross involving two autosomal genes with independent assortment, and we are evaluating whether the F2 phenotypic counts fit the 9:3:3:1 expectation. The observed counts are: Tall/Large = 104, Tall/Small = 17, Short/Large = 26, Short/Small = 13. The total number of plants is 160, and under independent assortment the expected counts are 90, 30, 30, and 10 respectively, since each class should occur in a 9:3:3:1 ratio. Now, for each option, I’ll compute or verify the chi-square components. Option A: The calculated chi-square value is 9.24, and the critical va......Login to view full explanation

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