Test a predeclared segregation ratio with an honest decision boundary

1. Frame the inheritance question

A genetic model predicts a distribution of offspring categories, not an exact finite count. Sampling variation can produce departures even when the model’s assumptions hold. A goodness-of-fit test compares the observed discrepancy with a reference distribution rather than deciding by whether the observed numbers equal the expected ratio exactly.

2. Explain mechanisms and assumptions

For exhaustive mutually exclusive categories, Pearson χ² sums (observed−expected)²/expected. Here 100 offspring are divided into recessive and other categories with a probability specified before observing them. With no fitted parameters, the two categories give one degree of freedom; the supplied 5% threshold is 3.841. Expected counts are sufficiently large throughout the bounded model.

A result above that threshold is evidence against the complete specified sampling model at the chosen rule. It is not the probability that the genetic hypothesis is false. A result below it is failure to reject, not proof that the named mechanism is uniquely correct. Another inheritance model can make similar predictions, particularly with small samples.

The complete model includes independent sampling, unbiased scoring and comparable viability, not only allele segregation. Differential survival, category misclassification or selecting offspring after seeing phenotypes can change counts. Preserve all categories and the original hypothesis. Searching many ratios after inspecting data changes the evidential interpretation and is not represented by this one-test threshold.

3. Work a quantitative example

For an expected 1:3 recessive-to-other ratio, expected counts are 25 and 75. Observed 35 and 65 give χ²=100/25+100/75=16/3≈5.333, exceeding 3.841. This challenges the supplied model but does not identify whether segregation, viability or scoring caused the discrepancy.

4. Predict and investigate

Predict first: If a test does not reject a ratio, has it proven the biological mechanism?

Compare recessive counts 25, 30 and 35 under expected fraction 0.25. Retain each contribution and the decision rule. Then choose the alternative 0.5 model only as a separately labeled hypothesis, not as a hidden post-hoc replacement of the original claim.

Retain the first prediction, settings, raw values and interpretation in the lesson notebook. All records are original supplied or calculated examples; no breeding, biological intervention or clinical inference is requested.

5. Apply the reasoning to a changed case

Apply the mechanism to a changed case

Under a fixed 1:1 two-category prediction for 100 offspring, observed counts are 60 and 40. Compute χ² and compare with the supplied one-df threshold 3.841.

Retain your calculation, units and assumptions in the lesson notebook before opening this public practice response.

Compare a worked response

Expected counts are 50 and 50; χ²=100/50+100/50=4. This exceeds 3.841, so the fixed model is rejected under that stated rule. The test does not determine the causal source of the departure.

6. Reflect and retain evidence

Name the conditioning event, count boundary and biological replication unit. Which independent observation could distinguish the inheritance mechanism from scoring, viability or environmental alternatives? A public worked response or saved prose does not establish independent assessment or supervised practical participation.

Sources and course continuation

Scientific supporting reference, checked 30 October 2026. Original prose and numerical cases; no source exercise or figure reproduced. Continue through General Biology I for mixed written evidence and the retained multistage project.