5 original questions · Application and evidence

Inheritance: expected counts and chi-squared

Use the context and data to draft a response, then compare your reasoning with an explanatory example.

Context and data

A cross between two heterozygous plants is modelled as Aa × Aa at one autosomal locus. A is completely dominant; segregation is normal, offspring observations are independent and survival does not differ by phenotype in the null model. Eighty offspring are classified. No model parameters are estimated from these observations. For this exercise, the 5% upper-tail critical chi-squared value for one degree of freedom is supplied as 3.841.

Observed phenotype counts
Phenotype	Observed count
Dominant	64
Recessive	16

Original illustrative data. Use the stated assumptions and units; these are not examination-board questions.

This worksheet includes questions and data, with space for your responses. Answers are omitted.

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Five questions

1. Calculate the expected phenotype counts under the stated null model.

2. Calculate χ² using Σ[(O − E)²/E]. Show the two contributions and round the total to three significant figures.

3. Determine the degrees of freedom for this fully specified two-category goodness-of-fit model.

4. Use the supplied critical value to assess whether these results reject the null model at the 5% level. State what the conclusion does not establish.