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 44.2 44.7 109 38.4 23 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: 6.3 6.9 5.9 5.5 6.5 6.1 5.3 5.4 8.4 6.2 8.5 Y: 12.8 14 11.6 11.2 12.8 11.9 12 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 11 12 13 14 15 16 17 18 19 20 Y: 21.2 21 21.2 21.1 21.4 21.5 21.7 21.7 21.7 21.9 22.1

c)
 X: 120 130 140 150 160 170 180 190 200 201 Y: 21.1 31 41.05 50.9 61.9 71 80.95 91.11 99.9 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):
 955 300 286 85
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)?