The Lady Tasting Tea By some accounts, the first formal hypothesis test to use statistics involved the claim of a lady tasting tea. In the 1920 's Muriel Bristol-Roach, a British biological scientist, was at a tea party where she claimed to be able to tell whether milk was poured into a cup before or after the tea. R.A. Fisher, an eminent statistician, was also attending the party. As a natural skeptic, Fisher assumed that Muriel had no ability to distinguish whether the milk or tea was poured first, and decided to test her claim. An experiment was designed in which Muriel would be presented with some cups of tea with the milk poured first, and some cups with the tea poured first.

(a) In plain English (no symbols), describe the null and alternative hypotheses for this scenario.

(b) Let \(p\) be the true proportion of times Muriel can guess correctly. State the null and alternative hypothesis in terms of \(p\).