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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. Being the gentleman that he is, 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 prefers her tea be poured first, then the milk. Fisher did not believe that the lady could tell the difference between "milk fırst" 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. Complete parts (a) to (e). (a) If we assume that the lady was simply guessing on whether the milk was first or not, what is the probability she would guess correct on any given cup? (b) Assuming guessing correct on one cup is independent of guessing correct on any other cup, what is the probability of guessing correctly on eight consecutive cups? (Round to four decimal places as needed.) (c) Explain how a coin could be used to simulate the random process of tasting eight cups of tea. The likelihood of obtaining a head with a fair coin is 0.75, which is the same as the likelihood of correctly guessing whether milk was put in the tea first or second.

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. Being the gentleman that he is, 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 prefers her tea be poured first, then the milk. Fisher did not believe that the lady could tell the difference between "milk fırst" 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. Complete parts (a) to (e). (a) If we assume that the lady was simply guessing on whether the milk was first or not, what is the probability she would guess correct on any given cup? (b) Assuming guessing correct on one cup is independent of guessing correct on any other cup, what is the probability of guessing correctly on eight consecutive cups? (Round to four decimal places as needed.) (c) Explain how a coin could be used to simulate the random process of tasting eight cups of tea. The likelihood of obtaining a head with a fair coin is 0.75, which is the same as the likelihood of correctly guessing whether milk was put in the tea first or second.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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. Being the gentleman that he is, 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 prefers 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. Complete parts (a) to (e). (a) If we assume that the lady was simply guessing on whether the milk was first or not, what is the probability she would guess correct on any given cup? (b) Assuming guessing correct on one cup is independent of guessing correct on any other cup, what is the probability of guessing correctly on eight consecutive cups? (Round to four decimal places as needed.) (c) Explain how a coin could be used to simulate the random process of tasting eight cups of tea. The likelihood of obtaining a head with a fair coin is 0.75, which is the same as the likelihood of correctly guessing whether milk was put in the tea first or second. (d) Use the coin-flipping applet in StatCrunch to simulate the experiment of Fisher 2000 times. Based on the simulation, what is the probability of correctly guessing on eight consecutive cups of tea? Open StatCrunch and select Applets Simulation-Coin flipping. Set "number of coins" to "8"; Set "number" to "=" and "8". Select "Use fixed seed" and use seed 1130. Click "Compute!" then click "1000 runs" twice to simulate 2000 times. Do not click "Reset" or any other buttons. The probability of correctly guessing on eight consecutive cups of tea is (Do not round.) (e) What do the probabilities from parts (b) and (d) suggest about the lady tasting tea? Choose the correct answer below. O A. The probability of the lady guessing the correct order of the milk in eight trials is very low. The evidence suggests she was not guessing. O B. The probability of the lady guessing the correct order of the milk in eight trials is high. The evidence suggests she was not guessing. OC. The probability of the lady guessing the correct order of the milk in eight trials is very low. The evidence suggests she was guessing. O D. The probability of the lady guessing the correct order of the milk in eight trials is high. The evidence suggests she was guessing.
Transcribed Image Text: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. Being the gentleman that he is, 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 prefers 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. Complete parts (a) to (e). (a) If we assume that the lady was simply guessing on whether the milk was first or not, what is the probability she would guess correct on any given cup? (b) Assuming guessing correct on one cup is independent of guessing correct on any other cup, what is the probability of guessing correctly on eight consecutive cups? (Round to four decimal places as needed.) (c) Explain how a coin could be used to simulate the random process of tasting eight cups of tea. The likelihood of obtaining a head with a fair coin is 0.75, which is the same as the likelihood of correctly guessing whether milk was put in the tea first or second. (d) Use the coin-flipping applet in StatCrunch to simulate the experiment of Fisher 2000 times. Based on the simulation, what is the probability of correctly guessing on eight consecutive cups of tea? Open StatCrunch and select Applets Simulation-Coin flipping. Set "number of coins" to "8"; Set "number" to "=" and "8". Select "Use fixed seed" and use seed 1130. Click "Compute!" then click "1000 runs" twice to simulate 2000 times. Do not click "Reset" or any other buttons. The probability of correctly guessing on eight consecutive cups of tea is (Do not round.) (e) What do the probabilities from parts (b) and (d) suggest about the lady tasting tea? Choose the correct answer below. O A. The probability of the lady guessing the correct order of the milk in eight trials is very low. The evidence suggests she was not guessing. O B. The probability of the lady guessing the correct order of the milk in eight trials is high. The evidence suggests she was not guessing. OC. The probability of the lady guessing the correct order of the milk in eight trials is very low. The evidence suggests she was guessing. O D. The probability of the lady guessing the correct order of the milk in eight trials is high. The evidence suggests she was guessing.
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