In an experiment concerning power of suggestion, participants are asked to pour

Question

In an experiment concerning power of suggestion, participants are asked to pour water into a large vase 200 ml capacity, as much or as little as they want, and given no further instructions. The participants are randomly selected to first or second, and the order is reversed. In one part of the experiment, the first participants are asked to pick up a jug containing 68 ml of water and pour it into the vase. Let the random variable X be the amount of water poured on the first attempt. The amount of water poured into the vase is slightly right skew with a mean of, E(X) = 39.3 ml, and SD(X) = 12.4 ml. Once the first participant pours water, they leave the room and a second participant is asked to pour water into the vase that water was already poured into, using another 68 ml jug of water. Let the random variable Y be the amount of water poured by the person going second. Suppose on the second pour attempt, by participant going second, the parameters are exactly the same as the first attempt: E(Y) = 39.3 ml and SD(Y) = 12.4 ml.

a. [3] Calculate E(X -Y)

b. [3] Calculate SD(X - Y) to two decimal places.

Explanation / Answer

Ans:

a)E[X-Y]=E[X]-E[Y]=39.3-39.3=0

b)Var(X-Y)=Var(X)+Var(Y)

          =12.42+12.42

        =307.52

SD(X-Y)=sqrt(307.52)=17.54

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