Problem 4 Who is the author? Statistics can help decide the authorship of literary works. Sonnets by a famous Elizabethan poet are known to contain an average of = 10.4 new words (words not used in the poet's other work). The number of new words in this poet's sonnets is normally distributed with standard deviation = 2.7. Now a manuscript with 5 new sonnets has come to light. Several scholars claim that these sonnets are the work of the famous Elizabethan poet. The new sonnets contain an average of X = 12.1 words not used in the poet's known works. Is this sufficiently strong evidence to reject the scholars' claim that the manuscript is by the Elizabethan poet? We will carry out a one-tailed hypothesis test. (4.3) Moderate Test the null hypothesis using both the critical value approach (also called the Z- test) and the p-value method, and confirm that they lead to the same conclusion. Use = 0.05. What do you conclude about the authorship of the new poems? Would your conclusion change if you were using a significance level = 0.1?