Statistic can help decide the authorship of literary works. Sonnets by a certain Elizabethan poet are known to contain an average 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 6 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 from 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 null hypothesis H0 : μ=8.9 against the alternative hypothesis HA : μ>8.9
a) Give the z test statistic and its P – value. What do you conclude about the authorship of the new poems?
b) What assumptions are you making when you carry out your test in a)?
