The Authorship of Ancient Writings Is Frequently in Dispute

Essay

The authorship of ancient writings is frequently in dispute. One method for judging authorship of writings from the Classical Greek period is to analyze the proportion of sentences containing the word, γα'ρ. (γα'ρ is an article, something like "a," "an," and "the" in English.) If a particular collection of works has markedly different frequencies of use of γα'ρ, this would be considered evidence against the same author having written all the works.
In the table below, data from random samples of 200 sentences each from 4 works are presented. The alleged author is one Philo Judaeus , a philosopher writing in ancient Alexandria, Egypt. ​
a)At the .05 level of significance, test the hypothesis that the frequencies of the use of γα'ρ is the same for these 4 works.
b)Write a short paragraph that could be added to a history or Classics Studies textbook that explains your results. Since your audience cannot be assumed to know any statistics, you must explain your conclusions and reasoning in, so to speak, "plain English."