Question

Please answer! This assignment is due in an hour.

When choosing an item from a group, researchers have shown that an important factor influencing choice is the item's location. This occurs in varied situations such as shelf positions when shopping, filling out a questionnaire, and even when choosing a preferred candidate during a presidential debate. In this experiment, five identical pairs of white socks were displayed by attaching them vertically to a blue background that was then mounted on an easel for viewing. One hundred participants from the University of Chester were used as subjects and asked to choose their preferred pair of socks. In choice situations of this type, subjects often exhibit the "center stage effect," which is a tendency to choose the item in the center. In this experiment, 34 subjects chose the pair of socks in the center. Are these data evidence of the "center stage effect"? Follow the four-step process (Hint: if subjects are choosing a pair of socks at random from the five positions, what would be the probability of selecting the pair in the middle? This is the value of p in the null hypothesis).

Answer 1

(a)
If each subject selects his or her preferred pair of socks at random, the probability that he or she would choose the pair of socks in the center position out of five identical pairs of white socks = 1/5 = 0.2
The correct distribution of X is,
X has a binomial distribution with parameters n=100 and p=1/5

(b)
Mean = np = 100 * (1/5) = 20
standard deviation =

(c)

Using normal approximation, the probability, P that 34 or more subjects would choose the item in the center if each subject were selecting his or her preferred pair of socks at random

P = P(X > 34) = P(Z > (34 - 20) / 4) = P(Z = 3.5) = 0.0002

Using R software, the exact binomial probability, Pe for 34 or more subjects would choose the item in the center

is, 0.0003

Both the probabilities, P and Pe are approximately equal.

d)

As, P or Pe is very low (near zero), if all participants were truly picking the socks at random, it is very unlikely that the 34 or more to choose the center pair. So, the correct answer is

The experiment supports the center stage effect. If participants were truly picking the socks at random, it would be highly unlikely for 34 or more to choose the center pair.