The authorship of ancient writings is frequently in dispute. One method for judg

Question

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, .p. ya is an article, something like "a," an," and "the" in English.) If a particular collection of works has markedly different frequencies of use of Ya'p, 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 of these works is Xenophon (c.428·c. 45 BCE), a Greek soldier Gar sentences Number of sentences in sample 200 200 200 200 Number of sentences Number of sentences Sam with without 36 39 37 17 164 161 163 183 ays and Means Commander t of Horsemanship icus a) At the.05 level of significance, test the hypothesis that the frequencies of the use of ya'p 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."

Explanation / Answer

R codes :

> cases=c(36,39,37,17)
> totcases=c(rep(200,4))
> prop.test(cases,totcases)

4-sample test for equality of proportions without continuity correction

data: cases out of totcases
X-squared = 11.636, df = 3, p-value = 0.00874
alternative hypothesis: two.sided
sample estimates:
prop 1 prop 2 prop 3 prop 4
0.180 0.195 0.185 0.085

a) Since p-value is small, we reject the null hypothesis of equality of 4 proportions at 5% level and conclude that the proportions are significantly unequal.

b) Here, we need to check if the proportions of ya'p are equal for 4 works. So we did a 4-sample proportion test, where we have a test statistic which is calculated based on the data given and we have a critical value. If the value of the test statistic is > critical value, we reject the null hypothesis H0 : p1=p2=p3=p4.
Another approach is we find the probability that the test statistic is > observed value of the test statistic here, when the null hypothesis is assumed to be true. This test statistic follows some known distribution which is why we get the values of the test statistic from some tables. This probability is known as p-value which if < 0.05, we reject H0 and if > 0.05, we accept H0 at 5% level of significance.

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