One of the first descriptions of a true randomized experiment was given by Ronal
ID: 3335273 • Letter: O
Question
One of the first descriptions of a true randomized experiment was given by Ronald Fisher in 1935 (The Design of Experiments). He described a tea party in Cambridge where a woman claimed that she could tell whether a cup of tea with milk had the milk added to the tea or the milk poured into the cup first and then the tea added. Fisher proposed an experiment to determine whether she truly could tell the difference.
a) Explain how randomization could be used in such an experiment.
b) If she is given one cup of tea, what is the probability that she could give the right answer even if she is only guessing?
c) Suppose she will be given 10 cups. Let X represent the number of cups for which she makes the correct identification of which ingredient was poured first. Under what conditions X be considered a binomial random variable? Are they reasonable for this situation?
d) What are the parameters of the binomial distribution in (c)? Explain why the exact value for one of the parameters is unknown.
e) Suppose that she is just guessing on each cup and also that she doesn’t know how many cups there are of each type. Use the One Proportion Inference applet to determine how many identifications she needs to get correct out of ten so that the probability of doing so by guessing is less than 0.05. Include a screen shot of the applet results in your solution.
(By the way – Fisher never said how many she did get correct!)
Explanation / Answer
(a) In such an experiment. An number of test can be given to the woman where he will be shown a cup of tea where she has to judge whether it is mil then tea or tea than milk in that cup. For randomization, only discrete made cup of tea has to be shown to jher.
(b) Proobability that she will give a right answer is 1/2 as there are only two options from which she has to choose.
(c) THe condition X to be considered a binomial random variable. Here the condition to be binomial is large population size or say number of cups must be too high in population from which this 10 cup of tea has been chosen. Each trial to be independent of each other that means that doesn't have any precondition notion about any cup of tea. Yes, thery are reasonable in this situation.
(d) Parameter(S) n = 10 and p = 0.5 (if she is totally guesing) here but we can't check it that she is guerssing or she has a prior knowledge that which of the component is addded first in the tea. If she just guess, the p = 0.5 .
(e) Here Pr(x> X; 10 ; 0.5) <= 0.05
so Here X = 8 that would be the minimum correct answers required to have a probability of doing so by guessing is less than 0.05.
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