Statistics can help decide the authorship of literary works. Sonnets by a well-known poet contain an average of μ = 6.9 new words (words not used in the poet’s other works) and a standard deviation of σ = 2.7 words, and the number of new words is approximately Normally distributed. Scholars expect sonnets by other authors to contain more new words than this famous poet’s works. A new manuscript has been discovered with many new sonnets, and scholars are debating whether it is this poet’s work.

They take a random sample of five sonnets from the new manuscript and count the number of new words in each one. The mean number of new words in these five sonnets is x¯ = 9.2.

The following dotplot shows the results of simulating 200 random samples of size 5 from a Normal distribution with a mean of 6.9 and a standard deviation of 2.7, and calculating the mean for each sample.

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest.

b. Use the simulation results to estimate the P-value of the test in part (a). Interpret the P-value.

c. What conclusion would you make?

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4.0 4.4 4.8 5.2 5.6 6.0 64 6.8 7.2 7.6 8.0 8.4 8.8 9.2 9.6 10.0 *= simulated mean number of new words .....·. ..... ..... ....