Answered: It appears that there is a significant…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

It appears that there is a significant relationship between cognitive ability and social rank, at least for birds. Boogert, Reader, and Laland (2006) measured social rank and individual learning ability for a group of starlings. The following data represent results similar to those obtained in the study.

Subject	Social Rank	Learning Score
A	1	3
B	3	10
C	2	7
D	3	11
E	5	19
F	4	17
G	5	17
H	2	4
I	4	12
J	2	3

Because social rank is an ordinal variable, the Spearman correlation is appropriate for these data. The social rank categories and the learning scores should both be converted to ranks before the correlation is computed. (Use three decimal places for the correlation.)

Subject	Social Rank	Learning Score
A	1	3
B	3	10
C	2	7
D	3	11
E	5	19
F	4	17
G	5	17
H	2	4
I	4	12
J	2	3

∑X	∑Y	SSXX	SSYY	∑XY	SP	rSS

Based on this correlation, is there a significant relationship between social rank and learning ability? Use a two-tailed test with α = .05.

df = n – 2	Level of Significance for One-Tailed Test
.05	.025	.01	.005
Level of Significance for Two-Tailed Test
.10	.05	.02	.01
1	.988	.997	.9995	.9999
2	.900	.950	.980	.990
3	.805	.878	.934	.959
4	.729	.811	.882	.917
5	.669	.754	.833	.874
6	.622	.707	.789	.834
7	.582	.666	.750	.798
8	.549	.632	.716	.765
9	.521	.602	.685	.735
10	.497	.576	.658	.708
11	.476	.553	.634	.684
12	.458	.532	.612	.661
13	.441	.514	.592	.641
14	.426	.497	.574	.623
15	.412	.482	.558	.606
16	.400	.468	.542	.590
17	.389	.456	.528	.575
18	.378	.444	.516	.561
19	.369	.433	.503	.549
20	.360	.423	.492	.537
21	.352	.413	.482	.526
22	.344	.404	.472	.515
23	.337	.396	.462	.505
24	.330	.388	.453	.496
25	.323	.381	.445	.487
26	.317	.374	.437	.479
27	.311	.367	.430	.471
28	.306	.361	.423	.463
29	.301	.355	.416	.456
30	.296	.349	.409	.449
35	.275	.325	.381	.418
40	.257	.304	.358	.393
45	.243	.288	.338	.372
50	.231	.273	.322	.354
60	.211	.250	.295	.325
70	.195	.232	.274	.302
80	.183	.217	.256	.283
90	.173	.205	.242	.267
100	.164	.195	.230	.254

Critical value of rs =

. This relationshipis significant.

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