1 Statistics
1.1 Calculate the mean of the following samples:
a)
| 12.3 |
14.7 |
12.4 |
15.3 |
12.4 |
11.6 |
15.5 |
13.3 |
13.9 |
11.2 |
16.8 |
b)
| 115 |
165 |
155 |
146 |
131 |
175 |
156 |
122 |
199 |
256 |
147 |
c)
| 17.3 |
1.8 |
63.0 |
44.2 |
44.7 |
109 |
38.4 |
23.0 |
99.2 |
56.3 |
45.6 |
22.4 |
1.2 Calculate the variance of the following samples:
a)
| 15.6 |
15.8 |
14.9 |
16.7 |
15.1 |
14.6 |
16.7 |
15.4 |
15.5 |
15.5 |
16.2 |
b)
| 5.6 |
4.6 |
2.7 |
2.8 |
7.5 |
4.7 |
3.2 |
2.2 |
5.6 |
4.7 |
8.4 |
4.3 |
4.4 |
5.1 |
3.9 |
c)
| 115 |
123 |
165 |
144 |
129 |
121 |
125 |
135 |
117 |
111 |
156 |
132 |
153 |
1.3 Calculate the correlation coefficient for each of the following sets of numbers:
a)
| X: |
12.2 |
13.2 |
11.4 |
12.5 |
12.9 |
13.5 |
13.1 |
12.9 |
11.6 |
11.8 |
13.9 |
| Y: |
12.6 |
12.9 |
11.9 |
12.8 |
12.4 |
12.9 |
13.2 |
12.8 |
11.8 |
11.6 |
13.9 |
b)
| X: |
6.30 |
6.90 |
5.90 |
5.50 |
6.50 |
6.10 |
5.30 |
5.40 |
8.40 |
6.20 |
8.50 |
| Y: |
12.8 |
14.0 |
11.6 |
11.2 |
12.8 |
11.9 |
12.0 |
11.1 |
17.1 |
12.8 |
16.5 |
c)
| X: |
100 |
124 |
116 |
118 |
130 |
122 |
117 |
125 |
105 |
| Y: |
200 |
176 |
184 |
182 |
170 |
178 |
183 |
175 |
195 |
1.4 Determine the slope and y-intercept of the best fit regression line for each of the following data sets:
a)
| X: |
12.3 |
14.6 |
19.7 |
18.5 |
13.9 |
18.1 |
17.9 |
16.6 |
14.6 |
15.5 |
18.6 |
18.5 |
| Y: |
17.7 |
15.6 |
10.4 |
11.5 |
16.5 |
11.6 |
12.2 |
14.1 |
15.4 |
14.4 |
11.3 |
11.8 |
b)
| X: |
10.0 |
11.0 |
12.0 |
13.0 |
14.0 |
15.0 |
16.0 |
17.0 |
18.0 |
19.0 |
20.0 |
| Y: |
21.2 |
21.0 |
21.2 |
21.1 |
21.4 |
21.5 |
21.7 |
21.7 |
21.7 |
21.9 |
22.1 |
c)
| X: |
120.0 |
130.0 |
140.0 |
150.0 |
160.0 |
170.0 |
180.0 |
190.0 |
200.0 |
201.0 |
| Y: |
21.10 |
31.00 |
41.05 |
50.90 |
61.90 |
71.00 |
80.95 |
91.11 |
99.90 |
99.99 |
1.5 Chi-square test
a) Use a chi-square test to determine if the following observed counts fit the theoretical distribution: 9:3:3:1 (critical value = 7.815):
b) A sample of tree snakes consisted of 45 males and 52 females. Test the hypothesis that there were an equal number of males and females (critical value = 3.841
1.6 t-test
a) Use a t-test to determine if the mean trait value differed between the two populations given below (critical value = 2.056):
| Population 1: |
4.5 |
6.5 |
4.7 |
3.6 |
5.2 |
4.6 |
7.6 |
8.4 |
8.1 |
4.3 |
2.1 |
6.4 |
5.6 |
3.4 |
| Population 2: |
2.3 |
4.6 |
7.5 |
4.6 |
5.2 |
8.5 |
2.6 |
6.3 |
5.8 |
8.1 |
7.3 |
6.6 |
5.4 |
1.5 |
b)You select for increased height in a group of plants. The initial population (before selection) consisted of 13 individuals with the following heights:
| 12.3 |
11.9 |
8.7 |
9.3 |
15.6 |
6.7 |
5.7 |
3.8 |
4.6 |
3.3 |
8.7 |
9.3 |
4.5 |
The heights of the 10 offspring of the chosen plants were:
| 10.3 |
9.5 |
8.7 |
8.8 |
9.9 |
9.2 |
10.1 |
14.6 |
13.6 |
13.9 |
Was a significant increase in plant height obtained (critical value = 2.080)?