Question

Charles Darwin (1876,The Effect of Cross- and Self-fertilization in the Vegetable Kingdom, 2nd Ed.,London: John Murray) described the results of an experiment to compare the heights of cornplants grown from seeds that resulted from cross-fertilization, with the heights of corn plantsgrown from seeds that resulted from self-fertilization.The seeds were placed in four pots, along two rows in each pot: one row had seeds of one kind,and the other row had seeds of the other kind, so that the plants were arranged in pairs, eachpair comprising one plant grown from a cross-fertilized seed, and one plant grown from a self-fertilized seed. Here are the heights of the fully grown plants, expressed in inches (1 inch = 2.54centimeter):

Pot	Self	Cross
1	139	188
1	163	96
1	160	168
2	160	176
2	147	153
2	149	172
3	149	177
3	122	163
3	132	146
3	144	173
3	130	186
4	144	168
4	102	177
4	124	184
4	144	96

The 15 self-fertilized plants had average height 140.6 inches, and standard deviation 16.4 inches.The 15 cross-fertilized plants had average height 161.5 inches, and standard deviation 28.9 inches.The average of the 15 differences in height between cross- and self-fertilized plants was 20.9inches, and the standard deviation of the same differences was 37.7 inches.

(a) Perform a Student?test of whether the mean heights are the same or different, disregardingthe pots the plants were planted in, and treating the self-fertilized and the cross-fertilizedplants as two independent samples.

b) Perform a Student?test of whether the mean heights are the same or different, again dis-regarding the pots the plants were planted in, but now using only the differences in heightbetween the plants in each pair.

(c) In (a), replace the Student?test by the Mann-Whitney test.

(d) In (b), replace the Student?test by the sign test.

(e) Compare the results.

Answer with formula and details and explanation.

Answer 1