Charles Darwin performed an experiment to determine if self-fertilized and cross-fertilized plants have different growth rates. Pairs of Zea mays plants, one self- and the other cross-fertilized, were planted in pots, and their heights were measured after a specified period of time. The data Darwin obtained were

(a) Calculate the paired differences and plot a dot diagram for the data. Does the assumption of normality seem plausible?
(b) Perform the Wilcoxon signed-rank test to determine if cross-fertilized plants have a higher growth rate than self-fertilized plants.

This approximation leads to a convenient form of a test for independence. Reject
H0 : X and Y are independent in favor of
Hi: Large values of X and Y tend to occur together and small values tend to occur together
if

Recall that za is the upper a point of a standard normal distribution. Two-tailed tests can also be conducted.

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