Question

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.

(a)

What is the level of significance?
=_______________

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

H₀: p = 0.261; H₁: p < 0.261

(b)

What sampling distribution will you use?

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

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

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

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

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.)

=_____________

Answer 1

a) The level of significance is 0.01

H0: P = 0.261

H1: P 0.261

b) np = 317 * 0.261 = 82.737

nq = 317 * (1 - 0.261) = 234.263

The standard normal, since np > 5 and nq > 5.

= 61/317 = 0.1924

The test statistic

  

c) P-value = 2 * P(Z < -2.78)

= 2 * 0.0027

= 0.0054