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 plants’ 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 μ and σ 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.
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