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 μ = 6.9 new words (words not used in the poet’s other works). The standard deviation of the number of new words is σ = 2.7. Now a manuscript with 5 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 = 11.2 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 H0: μ = 6.9 Ha: μ > 6.9 Give the z test statistic and its P-value. What do you conclude about the authorship of the new poems?

6.68 Study habits. The Survey of Study Habits and Attitudes

(SSHA) is a psychological test that measures the motivation, attitude toward school, and study habits of students. Scores range from 0 to 200. The mean score for U.S. college students is about 115, and the standard deviation is about 30. A teacher who suspects that older students have better attitudes toward school gives the SSHA to 25 students who are at least 30 years of age. Their mean score is x = 133.2.

(a) Assuming that σ = 30 for the population of older students, carry out a test of H0: μ = 115 Ha: μ > 115 Report the P-value of your test, draw a sketch illustrating the P-value, and state your conclusion clearly.

(b) Your test in

(a) required two important assumptions in addition to the assumption that the value of σ is known. What are they? Which of these assumptions is most important to the validity of your conclusion in (a)?