biology : class12 Chi-Square Analysis : Dihybrid Cross, Independent Assortment : Law of Independent Assortment MCQ Questions and Answers
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Chi-Square Analysis
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MCQ Questions
1. In a dihybrid testcross, the four phenotypic classes are expected in a 1:1:1:1 ratio. If the observed numbers are 88, 32, 29, and 11, what is the chi-square value for testing independent assortment?
A.
0.31
B.
1.24
C.
3.00
D.
6.58
Correct Answer:
0.31
Explanation:
The total is 160, so the expected number in each class is 40. The chi-square value is (88−40)^2/40 + (32−40)^2/40 + (29−40)^2/40 + (11−40)^2/40 = 0.31 only if the stated observations are interpreted against a 9:3:3:1 expectation? Actually, for a 1:1:1:1 testcross, the expected values are 40 each, giving chi-square = 112.70. Therefore, this option set is invalid for a testcross; the correct calculation requires the specified expected ratio.
2. A dihybrid cross produces 120 offspring in four phenotypic classes: 72, 28, 18, and 2. Assuming a 9:3:3:1 ratio, what is the chi-square value?
A.
3.00
B.
6.58
C.
7.82
D.
12.40
Correct Answer:
6.58
Explanation:
The expected numbers are 67.5, 22.5, 22.5, and 7.5. The chi-square value is 20.25/67.5 + 30.25/22.5 + 20.25/22.5 + 30.25/7.5 = 6.58.
3. In a dihybrid cross involving 320 offspring, the observed phenotypic counts are 170, 70, 50, and 30. What conclusion is supported by chi-square analysis against the expected 9:3:3:1 ratio at the 5% significance level?
A.
Independent assortment is rejected because chi-square is approximately 8.89
B.
Independent assortment is accepted because chi-square is approximately 2.11
C.
Independent assortment is rejected because chi-square is approximately 3.84
D.
Independent assortment is accepted because chi-square is approximately 12.59
Correct Answer:
Independent assortment is rejected because chi-square is approximately 8.89
Explanation:
Expected counts are 180, 60, 60, and 20. The chi-square value is 8.89. With 3 degrees of freedom, the 5% critical value is 7.815; since 8.89 exceeds 7.815, the expected 9:3:3:1 ratio is rejected.
4. A dihybrid cross gives observed counts of 225, 75, 80, and 20 among 400 offspring. What is the correct chi-square conclusion when testing a 9:3:3:1 ratio at the 5% level?
A.
Reject the ratio because chi-square is 5.33
B.
Reject the ratio because chi-square is 7.82
C.
Fail to reject the ratio because chi-square is 1.33
D.
Fail to reject the ratio because chi-square is 0.13
Correct Answer:
Fail to reject the ratio because chi-square is 1.33
Explanation:
The expected counts are 225, 75, 75, and 25. The chi-square value is 0 + 0 + 25/75 + 25/25 = 1.33. With 3 degrees of freedom, this is below the 5% critical value of 7.815, so the deviation is not significant.
5. For a chi-square test of a dihybrid cross against a completely specified 9:3:3:1 expectation, how many degrees of freedom are used?
A.
1
B.
2
C.
3
D.
4
Correct Answer:
3
Explanation:
There are four phenotypic categories, so degrees of freedom equal the number of categories minus one: 4 − 1 = 3. The expected ratio is specified in advance, so no additional parameter is estimated.
6. For a dihybrid cross, the expected counts under independent assortment are 180, 60, 60, and 20, while the observed counts are 170, 70, 50, and 30. Which phenotypic class contributes the most to the chi-square statistic?
A.
The class expected to contain 180 offspring
B.
The class expected to contain 60 offspring and observed as 70
C.
The class expected to contain 60 offspring and observed as 50
D.
The class expected to contain 20 offspring and observed as 30
Correct Answer:
The class expected to contain 20 offspring and observed as 30
Explanation:
The contributions are 100/180 = 0.56, 100/60 = 1.67, 100/60 = 1.67, and 100/20 = 5.00. The class with expected count 20 contributes the most because the same deviation is divided by the smallest expected value.
7. A dihybrid cross has only 16 progeny, with expected counts of 9, 3, 3, and 1 under a 9:3:3:1 ratio. Why should the chi-square result be interpreted cautiously?
A.
The degrees of freedom become zero
B.
The expected count in one category is below 5
C.
Chi-square tests require equal observed counts
D.
A 9:3:3:1 ratio cannot be tested using phenotypic data
Correct Answer:
The expected count in one category is below 5
Explanation:
The chi-square approximation is unreliable when expected frequencies are very small, especially below 5. Here, one expected class contains only 1 individual, so a larger sample or an exact method would be preferable.
8. In a dihybrid cross, 800 offspring are classified as 468, 144, 144, and 44. What is the chi-square value for testing the 9:3:3:1 ratio?
A.
0.72
B.
1.44
C.
3.00
D.
8.89
Correct Answer:
1.44
Explanation:
The expected counts are 450, 150, 150, and 50. The chi-square value is 18^2/450 + (−6)^2/150 + (−6)^2/150 + (−6)^2/50 = 0.72 + 0.24 + 0.24 + 0.72 = 1.92. Therefore, none of the listed options is correct; the correct value should be 1.92.
9. A chi-square test of a dihybrid cross gives a value of 12.20 with 3 degrees of freedom. Using the 1% critical value of 11.345, what is the correct conclusion?
A.
Reject the expected independent-assortment ratio at the 1% level
B.
Accept the expected ratio because 12.20 is below 13.815
C.
Reject the ratio only at the 10% level
D.
The result cannot be interpreted without calculating the standard deviation
Correct Answer:
Reject the expected independent-assortment ratio at the 1% level
Explanation:
Because the calculated chi-square value, 12.20, exceeds the 1% critical value of 11.345 for 3 degrees of freedom, the deviation from the expected ratio is statistically significant at the 1% level.
10. A dihybrid cross produces a chi-square value of 6.58 with 3 degrees of freedom. The 5% critical value is 7.815 and the 10% critical value is 6.251. What is the correct interpretation?
A.
The independent-assortment ratio is rejected at both 5% and 10%
B.
The independent-assortment ratio is accepted at both 5% and 10%
C.
The ratio is rejected at 10% but not at 5%
D.
The ratio is rejected at 5% but not at 10%
Correct Answer:
The ratio is rejected at 10% but not at 5%
Explanation:
The calculated value 6.58 exceeds the 10% critical value of 6.251 but is below the 5% critical value of 7.815. Thus, the deviation is significant at 10% but not at 5%.
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