The authorship of an old document is in doubt. A historian hypothesizes that the author was a journalist named Jacalyn Levine. Upon a thorough investigation of Levine’s known works, it is observed that one unusual feature of her writing was that she consistently began 10% of her sentences with the word “whereas.” To test the historian’s hypothesis, it is decided to count the number of sentences in the disputed document that begin with the word whereas. Out of the 300 sentences in the document, none begin with that word. Let p denote the probability that any one sentence written by the unknown author of the document begins with the word “whereas.”
a. Conduct a test of the hypothesis H0: p = 0.10 against Ha: p ≠ 0.10. What conclusion can you make, using a significance level of 0.05?
b. What assumptions are needed for that conclusion to be valid? (F. Mosteller and D. Wallace conducted an investigation similar to this to determine whether Alexander Hamilton or James Madison was the author of 12 of the Federalist Papers. See Inference and Disputed Authorship: The Federalist, Addison-Wesley, 1964.)