i12-48. A lady declares that by taking a cup of tea, she can discriminate whether the milk or tea infusion was first added to the cup. It is proposed to test this assertion by means of an experiment with 12 cups of tea, 6 made in one way and 6 in the other, and presenting them to the lady for judgement in a random order. (i) Calculate the probability that on the null hypothesis that the lady has no discrimination power, she would judge correctly all the 12 cups, it being known to her that 6 are of each kind. (ii) Suppose that the 12 cups were presented to the lady in six pairs, each pair to consist cups of each kind in a random order. How would the probability of correctly judging with every cup on the same null hypothesis be altered in this case ? Which of the two designs would you prefer and why ?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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i12-48. A lady declares that by taking a cup of tea, she can discriminate whether the milk or
tea infusion was first added to the cup. It is proposed to test this assertion by means of an experiment with
12 cups of tea, 6 made in one way and 6 in the other, and presenting them to the lady for judgement in a
random order.
(i) Calculate the probability that on the null hypothesis that the lady has no discrimination power, she
would judge correctly all the 12 cups, it being known to her that 6 are of each kind.
(ii) Suppose that the 12 cups were presented to the lady in six pairs, each pair to consist cups of each
kind in a random order. How would the probability of correctly judging with every cup on the same null
hypothesis be altered in this case ?
Which of the two designs would you prefer and why ?
Transcribed Image Text:i12-48. A lady declares that by taking a cup of tea, she can discriminate whether the milk or tea infusion was first added to the cup. It is proposed to test this assertion by means of an experiment with 12 cups of tea, 6 made in one way and 6 in the other, and presenting them to the lady for judgement in a random order. (i) Calculate the probability that on the null hypothesis that the lady has no discrimination power, she would judge correctly all the 12 cups, it being known to her that 6 are of each kind. (ii) Suppose that the 12 cups were presented to the lady in six pairs, each pair to consist cups of each kind in a random order. How would the probability of correctly judging with every cup on the same null hypothesis be altered in this case ? Which of the two designs would you prefer and why ?
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