Question

Symposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leach† found that about 21.4% of five-syllable sequences in Symposium are of the type in which four are short and one is long. Suppose an antiquities store in Athens has a very old manuscript that the owner claims is part of Plato's Dialogues. A random sample of 499 five-syllable sequences from this manuscript showed that 132 were of the type four short and one long. Do the data indicate that the population proportion of this type of five-syllable sequence is higher than that found in Plato's Symposium? Use α = 0.01.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: p = 0.214; H₁: p < 0.214H₀: p = 0.214; H₁: p ≠ 0.214    H₀: p = 0.214; H₁: p > 0.214H₀: p < 0.214; H₁: p = 0.214H₀: p > 0.214; H₁: p = 0.214

(b) What sampling distribution will you use?

The standard normal, since np < 5 and nq < 5.The standard normal, since np > 5 and nq > 5.    The Student's t, since np > 5 and nq > 5.The Student's t, since np < 5 and nq < 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.)


Sketch the sampling distribution and show the area corresponding to the P-value.

Answer 1