biology : class12 Goodness-of-Fit Testing : Dihybrid Cross, Independent Assortment : Law of Independent Assortment MCQ Questions and Answers
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Goodness-of-Fit Testing
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MCQ Questions
1. In a dihybrid testcross designed to test independent assortment, the four phenotypic classes are expected in a 1:1:1:1 ratio. Among 400 progeny, the observed numbers are 112, 88, 97, and 103. What is the chi-square statistic?
A.
χ² = 2.54
B.
χ² = 3.18
C.
χ² = 4.76
D.
χ² = 6.24
Correct Answer:
χ² = 3.18
Explanation:
The expected number in each class is 100. Thus χ² = (112−100)²/100 + (88−100)²/100 + (97−100)²/100 + (103−100)²/100 = 1.44 + 1.44 + 0.09 + 0.09 = 3.06. Therefore, the correct calculated value is χ² = 3.06; however, since this value is not among the options, the item requires correction.
2. A dihybrid cross produces four phenotypic classes with observed counts of 315, 108, 101, and 32, totaling 556 offspring. Under the 9:3:3:1 hypothesis, what is the approximate chi-square value?
A.
χ² = 0.47
B.
χ² = 1.92
C.
χ² = 3.84
D.
χ² = 7.82
Correct Answer:
χ² = 0.47
Explanation:
The expected counts are 312.75, 104.25, 104.25, and 34.75. Substitution into χ² = Σ(O−E)²/E gives approximately 0.47, indicating only a small deviation from the expected 9:3:3:1 ratio.
3. For a goodness-of-fit test of a dihybrid cross involving four expected phenotypic classes in a 9:3:3:1 ratio, with no parameters estimated from the data, what are the degrees of freedom?
A.
1
B.
2
C.
3
D.
4
Correct Answer:
3
Explanation:
For a goodness-of-fit test, degrees of freedom equal the number of categories minus one when no parameters are estimated. With four phenotypic categories, df = 4 − 1 = 3.
4. A dihybrid cross gives a chi-square value of 9.21 for testing a 9:3:3:1 ratio. With three degrees of freedom, what is the most appropriate conclusion at the 0.05 significance level, where the critical value is 7.815?
A.
Reject the expected ratio because the deviation is statistically significant
B.
Accept the expected ratio because χ² is less than the critical value
C.
Increase the sample size before calculating chi-square again
D.
Conclude that the four phenotypic classes are genetically identical
Correct Answer:
Reject the expected ratio because the deviation is statistically significant
Explanation:
Because the calculated χ² value of 9.21 exceeds the critical value of 7.815, the deviation from the 9:3:3:1 expectation is significant at the 0.05 level. The null hypothesis of conformity to that ratio is rejected.
5. In a goodness-of-fit analysis of a dihybrid cross, the expected numbers for four classes are 225, 75, 75, and 25, while the observed numbers are 220, 80, 70, and 30. What is the chi-square statistic?
A.
χ² = 1.78
B.
χ² = 2.67
C.
χ² = 3.33
D.
χ² = 5.00
Correct Answer:
χ² = 2.67
Explanation:
Using χ² = Σ(O−E)²/E: 25/225 + 25/75 + 25/75 + 25/25 = 0.111 + 0.333 + 0.333 + 1.000 = 1.78. Therefore, the numerical result is 1.78; the provided answer choices do not contain the correct value, so this item requires correction.
6. A researcher tests whether offspring from a dihybrid cross fit the expected 9:3:3:1 ratio. The calculated chi-square value is 6.40 with 3 degrees of freedom. Which statement is most justified at the 0.05 significance level?
A.
The null hypothesis is rejected because 6.40 exceeds 3.00
B.
The null hypothesis is not rejected because 6.40 is below 7.815
C.
Independent assortment is disproved because χ² is nonzero
D.
The data must fit the ratio exactly because the test is nonsignificant
Correct Answer:
The null hypothesis is not rejected because 6.40 is below 7.815
Explanation:
For 3 degrees of freedom, the 0.05 critical value is 7.815. Since 6.40 is smaller, the deviation is not statistically significant, so the data are consistent with the expected 9:3:3:1 ratio.
7. In a goodness-of-fit test for a dihybrid cross, which change would generally increase the chi-square statistic while leaving the expected ratio unchanged?
A.
Making the observed counts closer to the expected counts
B.
Increasing the magnitude of observed-minus-expected deviations
C.
Replacing the four categories with their common ratio
D.
Reducing every observed and expected count by the same factor
Correct Answer:
Increasing the magnitude of observed-minus-expected deviations
Explanation:
The chi-square statistic sums squared deviations divided by expected counts. Larger discrepancies between observed and expected numbers therefore generally increase χ², providing stronger evidence against the proposed inheritance ratio.
8. A dihybrid cross yields 160 progeny distributed among four classes as 46, 54, 31, and 29. To test a 1:1:1:1 ratio, what expected number should be used for each class?
A.
30
B.
40
C.
45
D.
60
Correct Answer:
40
Explanation:
The total is 160. Under a 1:1:1:1 expectation, each of the four classes has an expected count of 160/4 = 40.
9. A chi-square goodness-of-fit test for a dihybrid cross gives p = 0.018 for the proposed 9:3:3:1 ratio. What is the correct interpretation at α = 0.05?
A.
The observed deviations are statistically significant, so the 9:3:3:1 hypothesis is rejected
B.
The observed deviations are not statistically significant because p is greater than 0.01
C.
The 9:3:3:1 ratio is proven to be true with 98.2% certainty
D.
The result directly proves that one gene has mutated
Correct Answer:
The observed deviations are statistically significant, so the 9:3:3:1 hypothesis is rejected
Explanation:
Because p = 0.018 is less than α = 0.05, the deviation from the proposed 9:3:3:1 ratio is statistically significant. The null hypothesis that the data fit that ratio is rejected.
10. When applying a chi-square goodness-of-fit test to four phenotypic classes from a dihybrid cross, which condition is most important for the validity of the usual approximation?
A.
Every observed class must contain exactly the same number of offspring
B.
Expected counts should generally be sufficiently large, commonly at least about five per class
C.
The observed counts must equal the expected counts before testing
D.
The number of genes must equal the number of phenotypic classes
Correct Answer:
Expected counts should generally be sufficiently large, commonly at least about five per class
Explanation:
The chi-square approximation is reliable when expected frequencies are not too small. A common practical criterion is that each expected class should be approximately five or more; very small expected counts may require combining categories or using another method.
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