Chi-squared testAQA A-Level Biology: Subtopic test

1. 1
   A student crosses two heterozygous pea plants and expects a 3 : 1 ratio of round to wrinkled seeds in the offspring. She counts 400 seeds: 295 are round and 105 are wrinkled. She uses a chi-squared (χ²) test to compare her observed numbers with the numbers expected.

   (a)

   How many round seeds does she expect among the 400 seeds?

   [1 mark]

   • A100
   • B200
   • C300
   • D400

   (b)

   How many degrees of freedom should she use for the test?

   [1 mark]

   • A1
   • B2
   • C3
   • D4

   (c)

   Calculate χ² for her results. Use the formula χ² = Σ (O − E)² / E and give your answer to two decimal places.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A researcher crosses two fruit flies that are heterozygous for body colour and wing length. He expects the offspring to show a 9 : 3 : 3 : 1 phenotypic ratio. Among 160 offspring he counts 79 grey normal-winged, 40 grey vestigial-winged, 29 ebony normal-winged and 12 ebony vestigial-winged flies. He calculates χ² = 5.11. The critical value of χ² at p = 0.05 with 3 degrees of freedom is 7.82.

   (a)

   Which of these is a suitable null hypothesis for the researcher's test?

   [1 mark]

   • AThe flies show a 9 : 3 : 3 : 1 ratio exactly
   • BThe genes are linked
   • CThe observed numbers are significantly different from the expected numbers
   • DThere is no significant difference between the observed and expected numbers

   (b)

   How many degrees of freedom apply to this test?

   [1 mark]

   • A2
   • B3
   • C4
   • D16

   (c)

   State and explain the conclusion the researcher should draw from his result.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A student test crosses a fly heterozygous for two genes with a fly that is homozygous recessive for both genes. If the genes assort independently, a 1 : 1 : 1 : 1 ratio of four phenotypes is expected. Among 160 offspring there are 62 of the first phenotype, 58 of the second, 22 of the third and 18 of the fourth. The critical value of χ² at p = 0.05 with 3 degrees of freedom is 7.82.

   (a)

   State a null hypothesis for this investigation and explain how the number of degrees of freedom is found.

   [3 marks]

   (b)

   Calculate χ² for these results and state, with a reason, what the student should conclude.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   In mice, the gene with alleles $A$ (agouti) and $a$ (black) controls hair colour, and a second gene with alleles $C$ and $c$ controls whether pigment is made: $cc$ mice are albino whatever their genotype at the first gene. Two $AaCc$ mice are crossed repeatedly. In one batch of 320 offspring there are 168 agouti, 70 black and 82 albino mice, and the expected ratio is 9 agouti : 3 black : 4 albino. The critical value of χ² at p = 0.05 with 2 degrees of freedom is 5.99.

   (a)

   Calculate χ² for the results from the batch of 320 mice and state, with a reason, what you conclude.

   [6 marks]

   (b)

   A second batch of mice from the same cross gives χ² = 7.10. Evaluate whether this batch supports the 9 : 3 : 4 ratio, and suggest what the researcher could do next.

   [6 marks]

   Total for question 4: 12 marks

End of questions