Statistical analysis

Sample questions

Original practice questions written in the style of the exam.

1. Question 14 marks

   Students counted crab burrows in quadrats at increasing distances from the high-tide line on a beach.

   Distance from high-tide line / m	2	4	6	8	10	12	14	16
   Number of burrows	31	27	29	22	18	20	12	9

   Calculate Spearman's rank correlation coefficient using $r_s = 1 - \frac{6\sum d^2}{n(n^2 - 1)}$ and interpret the result. The critical value for $n = 8$ at the 5% significance level is 0.738.

   Mark scheme

   • Ranks both variables correctly, e.g. distance 1 to 8 and burrows 8, 6, 7, 5, 3, 4, 2, 1 (1)
   • $\sum d^2 = 164$ (1)
   • $r_s = 1 - \dfrac{6 \times 164}{8 \times 63} = -0.95$ (1)
2. Question 24 marks

   In a dihybrid cross the expected ratio of phenotypes is $9 : 3 : 3 : 1$. A student counted 160 offspring.

   Phenotype	1	2	3	4
   Observed	98	28	25	9

   Calculate $\chi^2$ using and state whether the results support the expected ratio. The critical value at the 5% significance level for 3 degrees of freedom is 7.82.

3. Question 34 marks

   The lengths of leaves were measured for 10 leaves from the sunny side and 10 leaves from the shaded side of a tree.

   	Sunny side	Shaded side
   Mean length / mm	20.8	24.6
   Standard deviation / mm	2.7	3.1
   Number of leaves	10	10

   Calculate $t$ using $t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}}$ and state a conclusion. The critical value for 18 degrees of freedom at the 5% significance level is 2.10.