Cambridge International A Level Biology Revision Guide

Cambridge International A Level Biology
Answers to end-of-chapter questions
s = 13 659
39
s = 116.486
39
s = 2.99 [4]
b s M = 2.99
40
s M = 2.99
6.32
s M = 0.47 [2]
c
Mean mass / g
100
80
60
40
20
0
Error bars represent
±2 × the standard deviation
Lemon fruits set 1 Lemon fruits set 2
[5]
d the error bars for the two sets of fruits do
not overlap; it is therefore possible that the
difference between them is significant, but
we cannot be sure about this; we would need
to do a further statistical test, such as a t-test,
to be able to answer this question; [3]
[Total: 14]
2 Formula for the t-test is:
x 1 – x 2
t =
2
s 1
n + s 2
2
1 n 2
All of these values are shown on page 476.
They are:
x 1 = 3.12
x 2 = 3.02
s 1 = 0.17
s 2 = 0.16
n 1 = 21
n 2 = 19
x 1 – x 2 =3.12 – 3.02 = 0.10
s 1 2 = 0.17 2 = 0.0289
so s 1 2 ÷ n 1 = 0.0289 ÷ 21 = 0.00138
s 2 2 = 0.16 2 = 0.0256
so s 2 2 ÷ n 2 = 0.0256 ÷ 19 = 0.00135
s 1 2 ÷ n 1 + s 2 2 ÷ n 2 = 0.00138 + 0.00135 = 0.00273
The square root of this value is 0.0522.
Therefore t = 0.10 ÷ 0.0522 = 1.92
Now work out the number of degrees of
freedom, v:
v = (n 1 – 1) + (n 2 –1) = (21 – 1) + (19 – 1) = 38
In the probability table for t on page 000, look
up the critical value of t at the 5% level for
this number of degrees of freedom. This is
the value in the >30 row, which is 1.96.
Our value of t is smaller than this. We would have
to move to the left in the table, towards the value
for the 10% confidence level, to get this value.
This means that the probability of the difference
between the two sets of data being caused by
chance is more than 0.05, or more than 5%. We
can therefore say that there is no significant
difference between the two sets of data. [10]
3 For species P:
x x – x (x – x) 2
10 –0.2 0.04
9 –1.2 1.44
11 0.8 0.64
7 3.2 10.24
8 2.2 4.84
14 –3.8 14.44
10 –0.2 0.04
12 –1.8 3.24
12 –1.8 3.24
total = 102
9 –1.2 1.44
mean x = 10.2 Σ(x – x) 2 = 39.60
n – 1 = 9
Σ (x – x) 2
s =
n – 1
s = 4.40
s = 2.10
Cambridge International AS and A Level Biology © Cambridge University Press 2014