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 500 five-syllable sequences from this manuscript showed that 131 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?

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)

Level of significance = 0.01

H0: p = 0.214

Ha: p > 0.214

Sample proportion = 131 / 500 = 0.262

Test statistics

z = - p / sqrt( p (1 - p) / n)

= 0.262 - 0.214 / sqrt( 0.214 * 0.786 / 500)

= 2.62

b)

p-value = P( Z > z)

= P( Z > 2.62)

= 0.0044

Since p-value > 0.01 level, we have sufficient evidence to reject H0 .

We conclude at 0.01 level that we have enough evidence to support the claim.