Question

Question)

A person claims to be able to tell by taste whether the milk was added to a cup of tea or the tea added to the milk. To test his claim, 2n cups of tea are made, n by each method, and presented for his judgement in random order. Assume that the person in fact has no talent, and merely divides the cups into two groups at random.

(a) Determine p, the probability that all the cups are classified correctly, as a function of n.

(b) If the experiment is repeated 10 times, what is the probability that all n cups will be correctly classified in at MOST one experiment?

(c) How large should n be in order that the probability in (b) will be at least 0.99?

(d) Describe the meaning of these calculations in the terminology of hypothesis testing.

Answer 1

(d) Null Hypothesis: Persons claim is wrong if probability in part(b) is atleast 0.99 when a sample of 12 cups of tea is made