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 281 ​trials, the touch therapists were correct 121 times. Use a 0.05 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?

Answer 1

H0: p = 0.50

Ha: p 0.50

Sample proportion = 121 / 281 = 0.4306

Test statistics

z = ( - p) / sqrt [ p( 1 - p) / n ]

= ( 0.4306 - 0.50) / sqrt ( 0.5 * 0.5 / 281 )

= -2.33

Critical values at 0.05 significance level = -1.96 , 1.96

Since test statstics falls in rejection region, Reject the null hypothesis.

We conclude that we have sufficient evidence to support the claim.