AP Biology: Chi-Square Tests in Genetics Practice Questions
Test yourself on AP Biology: Chi-Square Tests in Genetics with 12 original AP Exams practice questions. Pick an answer to see instant feedback and a full explanation.
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1. A genetic model predicts purple and white offspring in a 3:1 ratio. A researcher independently samples 160 offspring. What are the expected counts under this model, in purple-then-white order?
Explanation. The ratio has four parts. Multiplying 160 by 3/4 gives 120 purple offspring, and multiplying by 1/4 gives 40 white offspring. These expected counts come from the proposed model, rather than the observed proportions.
2. A goodness-of-fit analysis has observed counts of 132 purple and 28 white offspring, with expected counts of 120 and 40. Using chi-square = sum of (observed - expected)^2 / expected, what is the statistic?
Explanation. The purple category contributes 12 squared divided by 120, or 1.2. The white category contributes negative 12 squared divided by 40, or 3.6. Adding both contributions gives 4.8. The opposite signs do not cancel after squaring.
3. A goodness-of-fit test compares four offspring phenotype categories with a fully specified 9:3:3:1 ratio. No model parameters are estimated from these observations. How many degrees of freedom should be used?
Explanation. With four categories and a fully specified ratio, the degrees of freedom equal four minus one, or three. The fixed total count imposes one constraint. The numbers in the ratio are weights, not the number of categories.
4. For a valid goodness-of-fit test of a specified genetic ratio, chi-square is 4.8. The supplied critical value is 3.84 at a significance level of 0.05. Which conclusion follows?
Explanation. The statistic exceeds the supplied cutoff, so the data provide evidence against the proposed ratio at this significance level. This decision does not identify the biological cause of the departure or establish the probability that the model is true.
5. A valid chi-square goodness-of-fit test of an offspring ratio gives p = 0.32. The significance level was set to 0.05 before collecting data. Which interpretation is justified?
Explanation. Because 0.32 exceeds 0.05, this test does not provide sufficient evidence to reject the model. A nonsignificant result does not prove the proposed ratio, and the p-value is not the probability that the model is true.
6. A genetic model predicts phenotype probabilities of 9/16, 3/16, 3/16, and 1/16. For a sample of 32 independent offspring, which issue violates the stated classroom rule that every expected count must be at least five for the chi-square approximation?
Explanation. The expected counts are 18, 6, 6, and 2. The last count falls below the stated threshold. This checks expected counts under the model; having four categories or probabilities that sum to one is not itself a violation.
7. A student records the phenotype of each of 50 offspring on three consecutive days and treats all 150 entries as independent offspring in a goodness-of-fit test. What is the main problem?
Explanation. The same individual contributes three records, so the entries cannot be treated as 150 independently sampled offspring. Counting the records as independent inflates the apparent sample size. Repeated measurements need an analysis that accounts for their dependence.
8. A cross is tested against a specified 1:2:1 genotype ratio using 80 offspring. What expected counts should be entered for the three genotypes in that order?
Explanation. There are four ratio parts, with 20 offspring per part. The expected counts are therefore 20, 40, and 20. They sum to the sample size of 80, and the middle genotype has twice the expected count of either outer genotype.
9. A genotype category has an observed count of 18 and an expected count of 24. What is this category's contribution to Pearson's chi-square statistic?
Explanation. The difference is negative 6. Squaring gives 36, and dividing by the expected count of 24 gives 1.5. Each category contributes a nonnegative value; 36 alone omits the required division by the expected count.
10. Two samples are tested against the same 1:1 offspring ratio. Sample A has counts 55 and 45; sample B has counts 110 and 90. How do their Pearson chi-square statistics compare?
Explanation. For A, expected counts are 50 and 50, giving 25/50 + 25/50 = 1. For B, expected counts are 100 and 100, giving 100/100 + 100/100 = 2. The same proportional departure produces a larger statistic when the sample is larger.
11. Assuming a specified genetic model and the test's sampling assumptions are true, what does a chi-square goodness-of-fit p-value of 0.02 describe?
Explanation. The p-value measures the upper-tail probability of the test statistic under the null model and assumptions. It concerns outcomes at least as discrepant as the observed data. It does not assign probabilities to the model being true or to a particular biological mechanism.
12. A valid goodness-of-fit test rejects a proposed 9:3:3:1 offspring ratio. Which follow-up statement is most defensible?
Explanation. Rejection indicates that the observed distribution is inconsistent enough with the proposed ratio to warrant further investigation. Several biological or measurement processes could produce departures. The goodness-of-fit result alone cannot distinguish their causes.
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FAQ
How do I calculate expected offspring counts?
Convert each stated ratio part into a probability, then multiply by the total number of offspring. For a 3:1 ratio and 160 offspring, the expected counts are 120 and 40. Keep the category order consistent.
When is degrees of freedom equal to categories minus one?
For the goodness-of-fit exercises here, the category probabilities are specified in advance and no model parameters are fitted from the same observations. With k categories, use k minus one. Fitting parameters can change the degrees of freedom.
Does failing to reject a genetic ratio prove it correct?
No. It means the test did not find sufficient evidence against that ratio at the chosen significance level. Sample size and test assumptions affect what the experiment can detect, so interpret the result alongside the study design.