Symposium is part of a larger work referred to as Platos Dia

Symposium is part of a larger work referred to as Plato\'s Dialogues. Wishart and Leacht found that about 21.4% of ftive-sylable 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 idate that the lation proportion of this type of five-sylable sequence is higher than that found in Plato\'s Symposium? Use a -0.01 (a) What is the level of significance? State the null and alternate hypotheses O Ho: 0.214 O Ho: p 0.214; : p 0.214 Ho: > 0.214; HI : p-0.214 Mo: -0.214, HIP 5 and ng>s O The standard normal, since np > 5 and no The Student\'s t, since np

Solution

Here level of significance = 0.01

Null hypothesis is H0 : p = 21.4/100 = 0.214

Alternative hypothesis H1 : p > 0.214

where p is the population proportion.

q = 1 - 0.214 = 0.786

Option b) is correct.

We have to check the conditions that,

n*p = 499 * 0.214 = 106.786

n*q = 499 * 0.786 = 392.214

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

Option b) is correct.

p^ = x / n = 132 / 499 = 0..2645

The test statistic for testing hypothesis is,

Z = (p^ - p) / sqrt [p*q/n]

Z = (0.2695 - 0.214) / sqrt [ 0.214*0.786 / 499 ]

Z = 2.75

The test statistic value is 2.75

P-value we can find by using EXCEL.

EXCEL syntax :

=NORMSDIST(z)

where z is the test statistic value

P-value = 1 - 0.9970398 = 0.0030

Here option a) is correct.

P-value < alpha (0.01)

Reject H0 at 0.01 significance level.

Conclude that data are statistically significant.

Option a) is correct.

There is sufficient evidence at the 0.01 level to conclude that the true proportion of the five syllable sequence is higher than that in Plato\'s Symposium.