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Who is the author? Statistics can help decide the
Chapter , Problem 6.70(choose chapter or problem)
Who is the author? Statistics can help decide the authorship of literary works. Sonnets by a certain Elizabethan poet are known to contain an average of \(\mu=8.9\) new words (words not used in the poet’s other works). The standard deviation of the number of new words is \(\sigma=2.5\). 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
\(\begin{array}{l}
\text { H0: } \mu=8.9 \\
\text { Ha: } \mu>8.9
\end{array}\)
Give the z test statistic and its P-value. What do you conclude about the authorship of the new poems?
Questions & Answers
QUESTION:
Who is the author? Statistics can help decide the authorship of literary works. Sonnets by a certain Elizabethan poet are known to contain an average of \(\mu=8.9\) new words (words not used in the poet’s other works). The standard deviation of the number of new words is \(\sigma=2.5\). 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
\(\begin{array}{l}
\text { H0: } \mu=8.9 \\
\text { Ha: } \mu>8.9
\end{array}\)
Give the z test statistic and its P-value. What do you conclude about the authorship of the new poems?
ANSWER:
Step 1 of 2
Given data:
The sample size is \(n=6\). The sample mean is \(\bar{x}=10.2\), Population standard deviation is \(\sigma=2.5\). The Population mean is \(\mu=8.9\).
The aim is to test whether there is evidence that the average new sonnets are greater than 8.9
Null hypothesis:
The average new words in sonnets is equal to 8.9.
\(H_{0}: \mu=8.9\)
Alternative hypothesis:
The average new words in sonnets are greater than 8.9
\(H_{a}: \mu>8.9\)