Question

A​ 9-year-old girl did a science fair experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left​ hand, and then she asked the therapists to identify the selected hand by placing their hand just under her hand without seeing it and without touching it. Among 252 ​trials, the touch therapists were correct 109 times. Use a 0.10 significance level to test the claim that touch therapists use a method equivalent to random guesses. Do the results suggest that touch therapists are​ effective?

Identify the test statistic and P - value for this hypothesis test.

Answer 1

let us consider

H_o :p = 0.5

H₁ ; p 0.5 (because there 50% probability that either head comes or tail comes while tossing a coin )

here n = 252

and x = 109 so = 109/252 = 0.433

now using z statistic =

=

= 0.067 / 0.031 = 2.161

p value = 0.031

Since the p-value is greater than the level of significance, we accept ?0 and conclude on the basis of the given data that there is insufficient evidence to warrant rejection of the claim that touch therapists use a method equivalent to random guesses.
The result suggests that the touch therapist performed good than random guesses, so they appear to be effective.