Statistics can help decide the authorship of literary works. Sonnets by a certain Elizabethan poet are known to contain an avera

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Statistics can help decide the authorship of literary works. Sonnets by a certain Elizabethan poet are known to contain an avera

ge of μ = 8.9 new words (words not used in the poet’s other works). The standard deviation of the number of new words is σ = 2.5. Now a manuscript with six new sonnets has come to light, and scholars are debating whether it is the poet’s work. The new sonnets contain an average of x~ = 10.2 words not used in the poet’s known works. We expect poems by another author to contain more new words, so to see if we have evidence that the new sonnets are not by our poet we test the following hypotheses.
H0 : µ = 8.88 vs Ha : µ > 8.88
Give the z test statistic and its P-value. What do you conclude about the authorship of the new poems? (Let a = .05.)
Use 2 decimal places for the z-score and 4 for the p-value.
a. What is z?
b.The p-value is greater than?
c.What is the conclusion? A)The sonnets were written by another poet or b) There is not enough evidence to reject the null.

Mathematics

1 answer:

AnnZ [12.3K] · Answer 1 · 2026-04-07T07:59:22+03:00

Response:

It is inferred that the authors of the sonnets belong to a certain poet from the Elizabethan era.

Step-by-step breakdown:

The details provided in the question are as follows:

Population mean, μ = 8.9

Sample mean, $\bar{x}$ = 10.2

Sample size, n = 6

Alpha, α = 0.05

Population standard deviation, σ = 2.5

Initially, we formulate the null hypothesis and the alternative hypothesis

To conduct this test, we utilize the One-tailed z test.

a) Equation:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

By substituting in all relevant values, we determine:

$z_{stat} = \displaystyle\frac{10.2 - 8.9}{\frac{2.5}{\sqrt{6}} } = 1.28$

Next, $z_{critical} \text{ at 0.05 level of significance } = 1.64$

b) The p-value is computed using the z-table.

P-value = 0.1003

The p-value surpasses the alpha of 0.05

c) Because the p-value exceeds the alpha threshold, there is insufficient evidence to dismiss the null hypothesis, thereby supporting the null hypothesis.

Consequently, it is concluded that the authorship of the sonnets belongs to a particular Elizabethan poet.