Exercise 4.29 introduces a historical scenario in which a British woman, Muriel Bristol-Roach, claimed to be able to tell whether milk had been poured into a cup before or after the tea. An experiment was conducted in which Muriel was presented with 8 cups of tea, and for each cup she correctly guessed whether the milk was added first or the tea added first. Let's assume that Muriel did not know beforehand how many of the 8 cups had tea first and how many had milk first. Let \(p\) represent the true proportion of times Muriel can guess correctly. Our hypotheses are \(H_{0}: p=0.5\) (random guessing) and \(H_{a}: p>0.5\).

(a) Give the value and notation for the sample statistic.

(b) Use StatKey or other technology to generate a randomization distribution, and find the \(p\)-value.

Data From Exercise 4.29:

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.