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 498 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 ???? = 0.01.

Answer 1

Complete Question

ymposium 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 498 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 = 0.01.  

a. What is the value of the sample test statistic? (Round your answer to two decimal places.)  

b. Find the P-value of the test statistic. (Round your answer to four decimal places.)

Answer:

a) $Z=2.45$

b) $P Value=0.0073$

Step-by-step explanation:

From the question we are told that:

Probability of Wishart and Leach $P=21.4=>0.214$

Population Size $N=498$

Sample size $n=12$

Therefore

$P'=\frac{129}{498}$

$P'=0.2590$

Generally the Null and Alternative Hypothesis is mathematically given by

$H_0:P=0.214$

$H_a:=P>0.214$

Test Statistics

$Z=\frac{P'-P}{\sqrt{\frac{P(1-P)}{n}}}$

$Z=\frac{0.2590-0.214}{\sqrt{\frac{0.214(1-0.214)}{498}}}$

$Z=2.45$

Therefore P Value is given as

$P Value =P(Z\geq 2.45)$

$P Value =1-P(Z\leq 2.45)$

$P Value =1-0.99268525$

$P Value=0.0073$