Prose rhythm is characterized as the occurrence of five-syllablesequences in long passages of text. This characterization may beused to assess the similarity among passages of text and sometimesthe identity of authors. The following information is based on anarticle by D. Wishart and S. V. Leach appearing in Computer Studiesof the Humanities and Verbal Behavior (Vol. 3, pp. 90-99).Syllables were categorized 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 317 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? Use ? = 0.01.

(a) What is the level of significance? 0.01

State the null and alternate hypotheses.

H0: p = 0.261; H1: p > 0.261

H0: p ? 0.261; H1: p = 0.261

H0: p = 0.261; H1: p ? 0.261 CORRECT

H0: p = 0.261; H1: p < 0.261

(b) What sampling distribution will you use?

The standard normal, since n·p < 5 and n·q < 5.

The Student's t, since n·p > 5 and n·q > 5.

The standard normal, since n·p > 5 and n·q > 5.CORRECT

The Student's t, since n·p < 5 and n·q < 5.

What is the value of the sample test statistic? (Round youranswer to two decimal places.) _______???

(c) Find the P-value of the test statistic. (Round your answerto four decimal places.) _________????