At a summer tea party in the late 1920s, a lady claimed that she could determine by

Question:

At a summer tea party in the late 1920s, a lady claimed that she could determine by taste if tea had been poured into the milk or if milk had been poured into the tea. Sir Ronald Fisher, well known for his work in design of experiments, discussed how to test this lady€™s claim. The lady was asked to taste several cups in random order and identify each as tea first or milk first. Although the actual results were not published, rumor has it that the lady correctly identified every single cup.9
Let€™s assume that the lady was given 14 cups of tea in random order. She was told that half the cups had tea first and the other half had milk first. Table 6.10 provides hypothetical results.
Table 6.10 Results of the hypothetical tea-tasting study.

the study was designed with exactly seven tea first and seven milk first cups; thus, the row totals are fixed. In addition, since the lady was told this, it is reasonable to set her answers to have exactly seven tea first guesses and seven milk first guesses. Thus, the column totals are also fixed.
a. Use Table 6.6 to determine the name of this type of study design. b. Which type of statistical tests can be used with this study design?
c. Conduct a hypothesis test to determine if the lady could correctly identify the order in which items were poured into a cup. Submit a p-value and clearly state your conclusions.
d. Conduct a hypothesis test to determine if the lady could correctly identify the order in which items were poured into a cup. However, instead of using Table 6.10, assume she made four mistakes: She guessed tea first for two milk first cups, and she guessed milk first for two tea first cups. Based on the new data, submit a p-value and clearly state your conclusions.