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 265 trials, the touch therapists were correct 112 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 null and alternative hypotheses for this test. Choose the correct answer below. A. Upper H 0 : pequals0.5 Upper H 1 : pnot equals0.5 B. Upper H 0 : pnot equals0.5 Upper H 1 : pequals0.5 C. Upper H 0 : pequals0.5 Upper H 1 : pless than0.5 D. Upper H 0 : pequals0.5 Upper H 1 : pgreater than0.5

hypotheses test

p-value

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.5

H_a : p 0.5

n = 265

x = 112

= x / n = 112 / 265 = 0.4226

P₀ = 0.5

1 - P₀ = 1 - 0.5 = 0.5

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.4226 - 0.5 / [(0.5 * 0.5) / 265]

= -2.519

Test statistic = -2.519

P(z < -2.519) = 0.0059

P-value = 2 * 0.0059 = 0.0118

P-value = 0.0118