Study Figure 1 below.
This data in Figure 1 was collected to investigate whether there was a significant relationship between the percentage of silica and the percentage of volatile gases in lava samples, found at 12 contrasting volcanic locations.
Lava samples from 12 contrasting volcanic locations (n=12) |
% of silica in the lava |
Rank |
% of volatile gases* |
Rank |
d |
d2 |
1 |
50 |
9 |
1.9 |
11 |
−2 |
4 |
2 |
70 |
3 |
5.2 |
3 |
0 |
0 |
3 |
58 |
8 |
3.7 |
7 |
1 |
1 |
4 |
73 |
1 |
6.6 |
1 |
0 |
0 |
5 |
63 |
6 |
4.0 |
6 |
0 |
0 |
6 |
62 |
7 |
3.3 |
8 |
−1 |
1 |
7 |
45 |
12 |
3.0 |
9 |
3 |
9 |
8 |
71 |
2 |
4.1 |
5 |
−3 |
9 |
9 |
49 |
10 |
2.5 |
10 |
0 |
0 |
10 |
69 |
4 |
5.3 |
2 |
2 |
4 |
11 |
48 |
11 |
1.2 |
12 |
−1 |
1 |
12 |
68 |
5 |
4.5 |
4 |
1 |
1 |
|
|
|
|
|
∑d2 = |
|
Volatile gases – gases emitted by volcanoes at high temperature such as water vapour, carbon dioxide and sulphur dioxide.
a)
i)
Complete Figure 1 by calculating ∑d2
.
(1)
ii)
The formula for Spearman’s rank correlation coefficient value rs is given below; in this data set n is equal to 12.
rs = 1 −
Calculate the value of rs to two decimal places for the data given.
You must show your working.
(2)
iii)
The tables below show the two hypotheses that are being tested and the critical values of Spearman’s rank rs value when n = 12.
Null hypothesis: There is no significant relationship between the % of silica and the % of volatile gases in these lava samples. |
Alternative hypothesis: There is a significant relationship between the % of silica and the % of volatile gases in these lava samples. |
Confidence level |
0.10 (90% significance)
|
0.05 (95% significance) |
0.01 (99% significance) |
Critical value |
0.50 |
0.59 |
0.78 |
Using the Spearman’s rank correlation rs value calculated in (a)(ii), state which hypothesis can be accepted.
(1)