A Random Process—The Lady Tasting Tea
Ronald Fisher is considered the father of experimental design. Being of English descent, he was having afternoon tea with a colleague. The colleague’s wife entered the room as Fisher was pouring tea. Fisher offered tea to the lady. She politely accepted and requested milk with her tea. Fisher started to pour milk into the tea cup first, but the lady indicated that she preferred her tea be poured first, then the milk. Fisher did not believe that the lady could tell the difference between “milk first” versus “milk second” tea, but the lady insisted she could tell the difference. Being the consummate scientist, Fisher suggested an experiment in which he randomly put milk into the tea first in some instances, and milk into the tea second in others. It turns out, the lady tasting tea was correct in all eight trials.
c. Explain how a coin could be used to simulate the random process of tasting eight cups of tea.

Verified step by step guidance

1. Understand that the random process involves determining the order in which milk and tea are poured for each cup—either "milk first" or "milk second."
2. Assign one outcome of a coin toss to represent "milk first" (for example, heads) and the other outcome to represent "milk second" (for example, tails).
3. For each of the eight cups, toss the coin once to decide the pouring order randomly according to the assigned outcomes.
4. Record the result of each coin toss to keep track of the sequence of "milk first" and "milk second" cups presented to the lady.
5. This method ensures that the order of pouring is determined by a fair random process, simulating the random assignment in the experiment.

Key Concepts

Randomization in Experimental Design

Randomization is the process of assigning treatments or conditions to subjects by chance, reducing bias and ensuring that results are due to the treatment rather than other factors. In the tea tasting experiment, randomizing the order of 'milk first' or 'milk second' cups prevents predictable patterns and helps fairly test the lady's claim.

Simulation of Random Processes

Simulation uses a model or tool, like coin flips, to imitate a random process when actual experimentation is complex or impractical. Flipping a coin can represent two equally likely outcomes (e.g., milk first or milk second), allowing us to replicate the random assignment of tea cups in the experiment.

Hypothesis Testing and Random Trials

Hypothesis testing evaluates whether observed results are due to chance or a real effect. In the tea tasting case, the null hypothesis assumes the lady cannot distinguish the order of pouring. Conducting multiple random trials (eight cups) and analyzing outcomes helps determine if her success is statistically significant.