Solved:
Answered by AI, Verified by Human Experts
Statistics 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 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.
Statistics 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 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.
Answer:We conclude that the sonnets were written by by a certain Elizabethan poet.Step-by-step explanation:We aregiven the followingin the question:Population mean, μ = 8.9Sample mean,=10.2Sample size, n = 6Alpha, α = 0.05Population standard deviation, σ = 2.5First, wedesign the null and the alternate hypothesisWe useOne-tailed z testto perform this hypothesis.a) Formula:Putting all the values, we haveNow,b) We calculate the p value with the help of z-table.P-value = 0.1003Thep-value is greater than the significance level which is 0.05c) Since the p-value is greater than the significance level, there isnot enough evidence to reject the null hypothesis and accept the null hypothesis.Thus, we conclude that the sonnets were written by by a certain Elizabethan poet....