The authorship of an old document is in doubt. An academician hypothesizes that the author was a sociologist named Olivia Munn. Upon a thorough investigation of Munn’s known works, it is observed that one unusual feature of her writing was that she consistently began 5%

of her sentences with the word therefore. To test the academician’s hypothesis, it is decided to count the number of sentences in the disputed document that begin with therefore.

Out of the 400 sentences, none do. Let π denote the probability that any one sentence written by the unknown author of the document begins with therefore. Test H0:

π = 0.05 against Ha: π = 0.05.

What assumptions are needed for your conclusion to be valid?12