Nine-year-old Emily Rosa conducted this test: A professional touch therapist put both hands through a cardboard partition and Emily would use a coin flip to randomly select one of the hands. Emily would place her hand just above the hand of the therapist, who was then asked to identify the hand that Emily had selected. Touch therapists believed that they could sense the energy field and identify the hand that Emily had selected. The trial was repeated 280 times. (Based on data from “A Close Look at Therapeutic Touch,” by Rosa et al., Journal of the American Medical Association, Vol. 279, No. 13.)
a. Assuming that the touch therapists have no special powers and made random guesses, find the mean and standard deviation for the numbers of correct responses in groups of 280 trials.
b. The professional touch therapists identified the correct hand 123 times in the 280 trials. Is that result unusually low or high? What does the result suggest about the ability of touch therapists to select the correct hand by sensing an energy field?