In 1876, Charles Darwin had his book The Effect of Cross- and Self-Fertilization in the Vegetable Kingdom published. Darwin planted two seeds, one obtained by crossfertilization and the other by auto-fertilization, in two opposite but separate locations of a pot. Self-fertilization, also called autogamy or selfing, is the fertilization of a plant with its own pollen. Cross-fertilization, or allogamy, is the fertilization with pollen of another plant, usually of the same species. Darwin recorded the plantsâ€™ heights in inches. The data frame Fertilize from the PASWR package contains the data from this experiment.
(a) Create a variable DD defined as the difference between the variables Cross-fert and Self-fert.
(b) Perform an exploratory analysis of DD to see if DD might follow a normal distribution.
(c) Use the function fitdistr () found in the MASS package to obtain the maximum likelihood estimates of Î¼ and Ïƒ if DD did follow a normal distribution.
(d) Verify that the results from (c) are the sample mean and the uncorrected sample standard deviation of DD.