(1) Symposium is part of a larger workreferred to as Plato's Dialogues. Wishart and Leach†foundthat about 21.4% of five-syllable sequences in Symposiumare of the type in which four are short and one is long. Suppose anantiquities store in Athens has a very old manuscript that theowner claims is part of Plato's Dialogues. A random sampleof 488 five-syllable sequences from this manuscript showed that 128were of the type four short and one long. Do the data indicate thatthe population proportion of this type of five-syllable sequence ishigher than that found in Plato's Symposium? Useα = 0.01.
(a) What is the level of significance?_________
(b) What is the value of the sample teststatistic? (Round your answer to two decimal places.) ________
(c) Find the P-value of the teststatistic. (Round your answer to four decimal places.) ________
(2) Prose rhythm is characterized as theoccurrence of five-syllable sequences in long passages of text.This characterization may be used to assess the similarity amongpassages of text and sometimes the identity of authors. Thefollowing information is based on an article by D. Wishart and S.V. Leach appearing in Computer Studies of the Humanities andVerbal Behavior (Vol. 3, pp. 90-99). Syllables werecategorized as long or short. On analyzing Plato'sRepublic, Wishart and Leach found that about 26.1% of thefive-syllable sequences are of the type in which two are short andthree are long. Suppose that Greek archaeologists have found anancient manuscript dating back to Plato's time (about 427 - 347B.C.). A random sample of 316 five-syllable sequences from thenewly discovered manuscript showed that 61 are of the type twoshort and three long. Do the data indicate that the populationproportion of this type of five syllable sequence is different(either way) from the text of Plato's Republic? Useα = 0.01.
(a) What is the level of significance?_____________
(b) What is the value of the sample teststatistic? (Round your answer to two decimal places.)
(c) Find the P-value of the teststatistic. (Round your answer to four decimal places.)
