BUT YOU MUST SUMMARIZE THE RESULTS IN YOUR OWN WORDS IN A BLUEBOOK OR SEPARATE SHEETS OF PAPER. III. The Federalist papers were written in 1787-1788 by Alexander Hamilton, John Jay, and James Madison to persuade the citizens of the State of New York to ratify the constitution. Seventy-seven essays first appeared in several different newspapers, and then Hamilton wrote an additional eight essays designed to complete the job. Of the first 77 papers, it is generally agreed that Jay wrote five. Hamilton and Madison, as well as historians, seem agreed upon the authorship of an additional 57 papers, 43 by Hamilton and 14 by Madison. An additional three are usually referred to as "Hamilton and Madison." The authorship of another twelve is in flat dispute between Hamilton and Madison. In an effort to study the authorship of the disputed Federalist papers, two statisticians (Frederick Mosteller and David L. Wallace, in their Applied Bayesian and Classical Inference: The Case of the Federalist Papers, Springer-Verlag, 1964/1984) examined a few words for their ability to discriminate and for their consistency of rate. For this purpose, they discussed some results on 98 items of writing: 48 by Hamilton and 50 by Madison. One of the function words they examined is "to," on which the statisticians provide the following frequency distributions of rate per thousand words (i.e., the average occurrences of the word "to" per 1000 words in each item examined): Rate per 1000 words Hamilton Madison 20-25 0 25-30- N 30-35- 6 19 35-40- 14 12 40-45- 15 9 45-50- 8 2 50-55- HN 55-60 48 50 2It is calculated that for Hamilton, the mean rate per 1000 words is 40.73 with a standard deviation of 6.32, and for Madison, the mean rate per 1000 words is 35 .00 with a stande deviation of 6.00. Are these appropriate descriptive statistics for the two distributions? If not, what are? Explain these statistics in substantive terms by comparing the writing styles of Hamilton and Madison with respect to the use of "to"