In a large metropolitan hospital, cells from newborn babies are collected and examined microscopically over a 5-year period. Among approximately 7500 newborn males, six have one Barr body in the nuclei of their somatic cells. All other newborn males have no Barr bodies. Among 7500 female infants, four have two Barr bodies in each nucleus, two have no Barr bodies, and the rest have one. What is the cause of the unusual number of Barr bodies in a small number of male and female infants?
Table of contents
- 1. Introduction to Genetics51m
- 2. Mendel's Laws of Inheritance3h 37m
- 3. Extensions to Mendelian Inheritance2h 41m
- 4. Genetic Mapping and Linkage2h 28m
- 5. Genetics of Bacteria and Viruses1h 21m
- 6. Chromosomal Variation1h 48m
- 7. DNA and Chromosome Structure56m
- 8. DNA Replication1h 10m
- 9. Mitosis and Meiosis1h 34m
- 10. Transcription1h 0m
- 11. Translation58m
- 12. Gene Regulation in Prokaryotes1h 19m
- 13. Gene Regulation in Eukaryotes44m
- 14. Genetic Control of Development44m
- 15. Genomes and Genomics1h 50m
- 16. Transposable Elements47m
- 17. Mutation, Repair, and Recombination1h 6m
- 18. Molecular Genetic Tools19m
- 19. Cancer Genetics29m
- 20. Quantitative Genetics1h 26m
- 21. Population Genetics50m
- 22. Evolutionary Genetics29m
2. Mendel's Laws of Inheritance
Monohybrid Cross
Problem 18
Textbook Question
The following are F₂ results of two of Mendel's monohybrid crosses.

For each cross, state a null hypothesis to be tested using x² analysis. Calculate the x² value and determine the p value for both. Interpret the p-values. Can the deviation in each case be attributed to chance or not? Which of the two crosses shows a greater amount of deviation?

1
Step 1: State the null hypothesis for each cross. For Mendel's monohybrid crosses, the null hypothesis typically states that the observed phenotypic ratios follow the expected Mendelian ratio of 3:1 (dominant to recessive phenotype). So, for both (a) full vs. constricted pods and (b) violet vs. white flowers, the null hypothesis is: 'The observed phenotypic ratio fits a 3:1 Mendelian ratio.'
Step 2: Calculate the total number of offspring for each cross. For (a), add the counts of full pods and constricted pods: 882 + 299. For (b), add the counts of violet and white flowers: 705 + 224. These totals will be used to calculate the expected numbers under the 3:1 ratio.
Step 3: Calculate the expected numbers for each phenotype under the null hypothesis. Use the total number of offspring and multiply by the expected proportions: 3/4 for the dominant phenotype and 1/4 for the recessive phenotype. For example, expected full pods = total × 3/4, expected constricted pods = total × 1/4, and similarly for flowers.
Step 4: Use the chi-square formula to calculate the chi-square (χ²) value for each cross: , where O is the observed count and E is the expected count for each phenotype. Calculate this sum over both phenotypes for each cross.
Step 5: Determine the degrees of freedom (df) for the test, which is the number of phenotypic categories minus 1. Here, df = 2 - 1 = 1. Then, use a chi-square distribution table or calculator to find the p-value corresponding to the calculated χ² value and df = 1. Interpret the p-value: if p > 0.05, the deviation is likely due to chance and the null hypothesis is not rejected; if p < 0.05, the deviation is unlikely due to chance and the null hypothesis is rejected. Finally, compare the χ² values of the two crosses to determine which shows a greater deviation from the expected ratio.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Mendelian Monohybrid Cross and Expected Ratios
A monohybrid cross involves one gene with two alleles, typically showing a 3:1 phenotypic ratio in the F2 generation if one allele is dominant. Mendel's experiments demonstrated this pattern for traits like pod shape and flower color, which helps predict expected counts for each phenotype in genetic crosses.
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Monohybrid Cross
Chi-Square (χ²) Test for Goodness of Fit
The chi-square test compares observed data with expected data to determine if deviations are due to chance. It calculates a χ² value by summing the squared differences between observed and expected counts divided by expected counts. This test helps assess if observed genetic ratios fit Mendelian predictions.
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Interpreting p-values and Null Hypothesis in Genetics
The null hypothesis assumes no significant difference between observed and expected ratios, meaning deviations are due to chance. The p-value indicates the probability of observing such deviations if the null is true. A high p-value (>0.05) suggests chance deviations, while a low p-value (<0.05) implies other factors affect the results.
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