1. Why should expected frequencies be at least 5 in each category when using the chi-square test?

A. To simplify calculations B. To ensure the validity of statistical results C. To increase degrees of freedom D. To match phenotype proportions exactly

2. Which of the following is NOT a condition for using the chi-square test?

A. Data must be in frequency form B. Observations must be independent C. Expected frequency in each category should be less than 5 D. Categories reflect the theoretical expectations

3. What is the critical value of \( \chi^2 \) at 0.05 significance level with 1 degree of freedom?

A. 2.71 B. 3.84 C. 5.99 D. 7.82

4. What would be the degrees of freedom for a test with 4 phenotypic categories?

A. 2 B. 3 C. 4 D. 5

5. Which genetic phenomenon can cause mismatch between observed and expected ratios besides gene linkage?

A. Epistasis B. Random fertilization C. Independent assortment D. Homozygosity

6. What is indicated when a chi-square calculated value is less than the critical value?

A. Reject the null hypothesis B. Significant difference exists C. Observed data fits the expected distribution well D. Sample size is inadequate

7. What factor could cause a chi-square test to NOT fit expected Mendelian ratios?

A. Independent assortment B. Large sample size C. Gene linkage D. Pure dominance

8. What does the probability in genetics primarily measure?

A. The exact outcome of a genetic cross B. The likelihood of a specific genetic event occurring C. The total number of offspring produced D. The environmental effects on genes

9. Which test would be used to check if data follow a normal distribution?

A. Chi-square test B. Shapiro–Wilk test C. Anderson–Darling test D. Kolmogorov–Smirnov test

10. How do you calculate expected frequency in Mendelian genetics?

A. Multiply total offspring by probability of phenotype B. Divide total offspring by the number of phenotypes C. Add observed counts of all phenotypes D. Subtract observed from total offspring

11. In a dihybrid cross (AaBb × AaBb), what is the probability of producing offspring with genotype aabb?

A. 1/4 B. 1/8 C. 1/16 D. 1/32

12. Which of the following is a common Mendelian phenotypic ratio tested with chi-square?

A. 2:1 B. 5:3 C. 9:3:3:1 D. 4:1

13. Why is it important that expected frequencies are at least 5 in each category for the chi-square test?

A. To ensure calculations are easier B. So that the test's approximation to the chi-square distribution is valid C. To increase degrees of freedom D. To reduce observed frequencies

14. Environmental factors can lead to which of the following outcomes in chi-square testing?

A. Perfect Mendelian ratio fit B. Gene linkage effects C. Deviation from expected genetic ratios D. Increased degrees of freedom

15. What hypothesis is tested in a chi-square goodness of fit test?

A. Observed data do not fit the expected distribution (H₁) B. Observed data fit the expected distribution (H₀) C. Both H₀ and H₁ are false D. There is a causal relationship between variables

16. What are the degrees of freedom (df) used for in a chi-square test?

A. To estimate the number of observed categories B. To determine the number of estimated parameters C. To calculate critical values for hypothesis testing D. To record the total sample size

17. In a test cross Aa × aa, what is the expected phenotypic ratio?

A. 3 Aa : 1 aa B. 1 Aa : 1 aa C. 9:3:3:1 D. 1:2:1

18. The chi-square formula (χ²) includes terms of the form (O - E)² / E. What do O and E represent?

A. O is original data and E is error margin B. O is observed frequency and E is expected frequency C. O is outcome frequency and E is environmental factor D. O is observed phenotype and E is experimental value

19. What does probability measure in genetics?

A. The certainty of an event occurring B. The likelihood of an event occurring C. The frequency of allele inheritance D. The number of offspring produced

20. If in a monohybrid cross the observed data significantly deviate from the expected 3:1 ratio, what might that indicate?

A. Sample size was too large B. Other genetic factors or environmental effects may be influencing C. Mendelian genetics apply perfectly D. The test cross was invalid

21. What is the expected frequency of "Round" phenotype in a monohybrid cross of Rr × Rr with 400 offspring if the expected ratio is 3:1?

A. 400 B. 100 C. 300 D. 200

22. What is the sum rule for probabilities of mutually exclusive events?

A. \( P(A \text{ or } B) = P(A) \times P(B) \) B. \( P(A \text{ or } B) = P(A) + P(B) \) C. \( P(A \text{ and } B) = P(A) + P(B) \) D. \( P(A \text{ and } B) = P(A) + P(B) - P(A \cap B) \)

23. Which of the following is NOT a type of probability?

A. Theoretical Probability B. Experimental Probability C. Chemical Probability D. Subjective Probability

24. Which rule of probability is used when calculating the likelihood of either one event or another occurring, but not both?

A. Product rule B. Sum rule C. Law of segregation D. Epistasis

25. What is the sum of expected values in a genetic cross?

A. Equal to the total number of observed individuals B. Always less than observed individuals C. Equal to the number of categories D. Always 1

26. What does a "good fit" in a chi-square test imply about Mendel’s laws?

A. Mendel's laws are rejected B. Mendelian inheritance likely applies C. Genetics follow no pattern D. Other unknown factors influence inheritance

27. In a monohybrid cross (Rr × Rr), what phenotypic ratio does Mendel predict?

A. 1:1 B. 3:1 C. 9:3:3:1 D. 1:2:1

28. What does the chi-square (\( \chi^2 \)) test primarily determine in genetics?

A. The exact genotype of offspring B. If observed data fit expected Mendelian ratios C. The dominance of alleles D. The number of alleles present

29. Which of the following does NOT describe the application of probability in genetics?

A. Predicting phenotype ratios B. Estimating carrier probabilities C. Determining allele dominance directly D. Testing Mendel’s laws

30. The rule of multiplication in probability applies to what type of events?

A. Dependent events B. Mutually exclusive events C. Independent events D. Overlapping events

31. What is the formula for calculating the chi-square statistic?

A. \( \chi^2 = \sum \frac{(O - E)^2}{E} \) B. \( \chi^2 = \sum (O + E) \) C. \( \chi^2 = \frac{O}{E} \) D. \( \chi^2 = (O - E) \times E \)

32. In a chi-square test, what do "O" and "E" represent, respectively?

A. Observed and estimated frequencies B. Observed and expected frequencies C. Overlap and error rates D. Outcome and event probabilities

33. When using the chi-square test, what does it mean if \( \chi^2_{calculated} < \chi^2_{critical} \)?

A. Reject the null hypothesis; poor fit B. Fail to reject the null hypothesis; good fit C. Null hypothesis is true with 100% certainty D. There is a significant difference between observed and expected

34. Which of these is a commonly tested Mendelian phenotypic ratio?

A. 2:1 B. 5:3:2 C. 3:1 D. 7:1

35. When performing a chi-square test, what does a good fit between observed and expected data suggest?

A. The data supports Mendelian inheritance laws B. Other genetic influences are significant C. The sample size is too small D. Mutations have altered the outcome

36. Which goodness of fit test is stronger than the Kolmogorov–Smirnov test for detecting differences in distribution tails?

A. Anderson–Darling test B. Shapiro–Wilk test C. Likelihood ratio test D. Chi-square test

37. How are degrees of freedom (df) calculated for a chi-square goodness of fit test?

A. \( df = k \) B. \( df = k + 1 \) C. \( df = k - 1 \) D. \( df = k - 2 \)

38. Which statistical test would you use to check if a die is fair?

A. T-test B. Chi-square goodness of fit test C. ANOVA D. Regression analysis

39. If a chi-square test results in a poor fit, what might be a reason related to data collection?

A. Large sample size B. Incorrect classification of phenotypes C. Proper experimental controls D. Random mating

40. Which is a correct interpretation of \( \chi^2 = 1.33 \) with df=1 and critical value 3.84?

A. Significant difference exists B. No significant difference; data fit expected values C. Test is inconclusive D. Data are invalid

41. What expected phenotypic ratio corresponds to a monohybrid cross of heterozygotes (Rr × Rr)?

A. 1:1 B. 3:1 C. 1:2:1 D. 9:3:3:1

42. Which formula correctly calculates the probability of two independent events both occurring?

A. \( P(A \text{ or } B) = P(A) + P(B) \) B. \( P(A \text{ and } B) = P(A) \times P(B) \) C. \( P(A \text{ and } B) = P(A) + P(B) - P(A \cap B) \) D. \( P(A \text{ or } B) = P(A) \times P(B) \)

43. How is the expected frequency for a category calculated in chi-square testing?

A. By multiplying the observed frequency by the number of categories B. By dividing total observations by the number of categories C. Based on the theoretical probability times the total number of observations D. By subtracting observed frequency from total observations

44. What does a chi-square test help differentiate in genetic data analysis?

A. Dominant from recessive alleles B. Random variation from significant genetic effects C. Genotypic proportions from phenotypic proportions D. Crossing over events from mutations

45. Which of the following best describes "mutually exclusive events"?

A. Events that cannot occur at the same time B. Events that must both occur C. Events that are independent D. Events that overlap partially

46. In a dihybrid cross AaBb × AaBb, what is the probability of offspring genotype aabb?

A. \( \frac{1}{4} \) B. \( \frac{1}{8} \) C. \( \frac{1}{16} \) D. \( \frac{1}{32} \)

47. What is the purpose of performing a goodness of fit test in genetics?

A. To identify gene mutations B. To assess if observed data matches expected genetic ratios C. To calculate allele frequencies D. To determine environmental influences on phenotype

48. What does the null hypothesis (H₀) state in a goodness of fit test?

A. Observed data do not fit the expected distribution B. Observed data fit the expected distribution C. There is environmental influence on phenotype D. Genetic linkage affects the outcome

49. According to the product rule, how is the probability of independent genetic events calculated?

A. By adding the probabilities B. By multiplying the probabilities C. By subtracting smaller probabilities from larger ones D. By dividing the probabilities

50. What is the null hypothesis (\(H_0\)) in a goodness of fit test?

A. Observed data do not fit the expected model B. Observed data fit the expected model C. The model is incorrect D. There is a significant difference in data