I NEED THIS ANSWERED ASAP!! THANK YOU IN ADVANCE!!

Question

Muriel Bristol says that milk should be poured first into tea and, conversely, that tea should NOT be poured into milk and that she can tell the difference. To test this claim, outside of the view of Muriel, a researcher lays out 8 cups of tea, 4 of which have tea poured first, and 4 of which have milk poured first. Muriel is asked to taste all 8 cups of tea and select the 4 cups in which milk was poured first.

The researcher makes the following hypothesis: Muriel cannot distinguish the cups with milk poured first from those with tea poured first and thus would be selecting 4 cups from the 8 total essentially at random.

(a) Show work to determine the number of different ways that 4 different cups could be selected from 8 total.

(b) In the experiment, Muriel did correctly identify all 4 cups in which milk had been poured first. What is the probability of this outcome assuming she had been selecting the cups at random?

(c) Is this statistically significant at the 0.05 level? Explain.

(d) What is the appropriate conclusion from this experiment? Explain in non-technical terms.

Answer 1

Hi Jalynn D.,

I would guess that you have moved on beyond this topic. But if not:

a) # ways of selecting 4 cups = combinations C(8,4) = 70.

b) P = 1/70 (she did in fact select the one combination that was what she said!)

c) here's where you must apply statistics. What kind of a result is this? Would you expect the results to follow a binomial distribution of # cups correct, if randomly selected (i.e., without actually being able to tell)? IF that were the case, that would imply a 1:4:6:4:1 distribution of outcomes of (0:1:2:3:4) cups correctly picked, or 1/16 probability of getting what she did. But this is incorrect and deceptive, because it assumes that each "draw" is from an infinite pool of 1/2 correct cups. But the pool is NOT infinite. So the probability of picking "correct" cups goes as (4/8)*(3/7)*(2/6)*(1/5) or 1/70, which agrees with (a). Now, how likely is this, and what kind of a normal distribution (i.e. what is std dev?) do we have? Now, that's not really a fair question, is it, since we have a distribution of expected results which is discrete rather than continuous. So you MIGHT need to do a little calculation, in order to apply a normal distribution statistic.

Hope this helped you along a little, anyway.

-- Cheers, __mr. d.