Prose rhythm is characterized as the occurrence of five-syllable
sequences in long passages of text. This characterization may be
used to assess the similarity among passages of text and sometimes
the identity of authors. The following information is based on an
article by D. Wishart and S. V. Leach appearing in Computer Studies
of the Humanities and Verbal Behavior (Vol. 3, pp. 90-99).
Syllables were categorized as long or short. On analyzing Plato's
Republic, Wishart and Leach found that about 26.1% of the
five-syllable sequences are of the type in which two are short and
three are long. Suppose that Greek archaeologists have found an
ancient manuscript dating back to Plato's time (about 427 - 347
B.C.). A random sample of 317 five-syllable sequences from the
newly discovered manuscript showed that 61 are of the type two
short and three long. Do the data indicate that the population
proportion of this type of five syllable sequence is different
(either way) from the text of Plato's Republic? Use α = 0.01. What
is the value of the sample test statistic? (Round your answer to
two decimal places.)
(c) Find the P-value of the test statistic. (Round your answer to
four decimal places.)