Statistics can help decide the authorship of literary works. Sonnets by a certain Elizabethan poet are known to contain an average of Î¼ = 6.9 new words (words not used in the poetâ€™s other works). The standard deviation of the number of new words is Ïƒ = 2.7. Now a manuscript with 5 new sonnets has come to light, and scholars are debating whether it is the poetâ€™s work. The new sonnets contain an average of x = 11.2 words not used in the poetâ€™s known works. We expect poems by another author to contain more new words, so to see if we haveevidence that the new sonnets are not by our poet we test
H0: Î¼ = 6.9
Ha: Î¼ > 6.9
Give the z test statistic and its P-value. What do you conclude about the authorship of the new poems?