Question

In Computer Studies of the Humanities and Verbal Behavior, D Wishart and SV Leach found that 21.4% of passages in Plato's Dialogues follow a particular syallable pattern, An owner of an antiquities store in Athens claims to have a manuscript that is a part of Dialogues. A random sample of 493 passages from the manuscript showed that 136 exhibited Plato's sy;;ab;e pattern. Do the data indicate this manuscript is part of Plato's Dialogues?

Answer 1

Let p denotes the true proportion of of passages in this manuscript.

To test $H_0: p = 0.214$ against $H_1: p \neq 0.214$

Here

sample proportion $\hat{p} = \frac{136}{493}= 0.2759$

and sample size n = 493

The test statistic can be written as

$z =\frac{\hat{p} - 0.214}{\sqrt{\frac{0.214*(1-0.214)}{n}}}$ which under H₀ follows a standard normal distribution.

We reject H₀ at 5% level of significance if $|z_{obs}|>z_{0.025}$

Now,

The value of the test statistic = $z_{obs} = 3.35117$

and critical value $z_{critical} = \pm z_{0.025} = \pm 1.95996$

Since $|z_{obs} |= 3.35117 > 1.95996$ , so we reject H₀ at 5% level of significance and we can conclude that there is sufficient evidence that this manuscript is significantly different from Plato's Dialogues.