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 485 five-syllable sequences from this manuscript showed that 129 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.

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

Solution :

Given that,

= 0.214

1 - = 0.786

n = 485

x = 129

Level of significance = = 0.01

Point estimate = sample proportion = = x / n = 0.266

This a right (One) tailed test.

Ho: p = 0.214

Ha: p 0.214

Test statistics

z = ( - ) / *(1-) / n

= ( 0.266 - 0.214) / (0.214*0.786) / 485

= 2.79

P-value = P(Z>z)

= 1 - P(Z <z )

= 1- P(Z < 2.79)

= 1 - 0.9974

= 0.0026

The p-value is p = 0.0026, and since p = 0.0026 < 0.01, it is concluded that the null hypothesis is rejected.