Chapter 8.3, Problem 15P

For Problems 7–21, please provide the following information.

1. (a) What is the level of significance? State the null and alternate hypotheses.
2. (b) Check Requirements What sampling distribution will you use? Do you think the sample size is sufficiently large? Explain. Compute the value of the sample test statistic and corresponding z value.
3. (c) Find the P-value of the test statistic. Sketch the sampling distribution and show the area corresponding to the P-value.
4. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
5. (e) Interpret your conclusion in the context of the application.

Plato’s Republic: Syllable Patterns Prose rhythm is characterized by 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.