Statistics can help decide the authorship of literary works. Sonnets by an Elizabethan poet are known to contain an average of ? = 6.9 new words (words not used in the poet's other works). The distribution of new words in this poet's sonnets is Normal with standard deviation ? = 2.7. Now a manuscript with five new sonnets has come to light, and scholars are debating whether it is the poet's work. The new sonnets contain an average of ? = 9.2 words not used in the poet's known works. We expect poems by another author to contain more new words. State the hypotheses and identify the claim.

1)State the hypotheses and identify the claim.

The claim is sonnets by an Elizabethan poet are known to contain an average of 6.9 new words.

The null and alternative hypotheses:

Ho: u = 6.9

H1: u > 6.9

2) Given an a=0.05, what type of test is used (left tailed, right tailed or two-sided tail) and what is the critical z-value? This is a right tailed test, since we know ?, we use z test. Critical z- value is 1.645

3.Compute the test value.

Z = (9.2 - 6.9) / (2.7 / sqrt 5) Z = 1.905

P value = 0.0287

4.Make the decision.

We reject the null hypothesis since our p value is so small (0.0287 < 0.05).

5.Summarize the results.

We reject the null hypothesis because there is sufficient evidence to support the claim. Therefore, we can conclude that it is possible that these poems were written by a new author because it looks to be very likely that they used more than 6.9 new words.