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 279 ​trials, the touch therapists were correct 118 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?

Answer 1

The calculated value z = 2.65>1.64 at 90% of level of significance

we reject null hypothesis at 10 % level of significance

The therapists use a method is not equivalent to random guesses

Explanation:

Step1:-

Given n = 279

Among 279 ​trials, the touch therapists were correct 118 times

Proportion of success 'p' = 118/ 279 = 0.4229

She flipped a coin to select either her right hand or her left​ hand

The Population proportion P = 1/2 = 0.5

level of significance level ∝ = 0.10

Null hypothesis H₀: P = 0.5

Alternative hypothesis H1: P ≠ 0.5

Q =1-P = 0.5

Step2:-

The z- statistic

Z = p-P/ S.E

where standard error of proportion

S.E = √PQ/n

S.E = 0.029

z = 0.4229-0.5/0.029 = -2.65

|z|=|-2.65|=2.65

Conclusion:-

The calculated value z = 2.65

The tabulated value z = 1.64 at 10% 0r 90% of level of significance

The calculated value z = 2.65>1.64 at 90% of level of significance

we reject null hypothesis at 10 % level of significance

The therapists use a method is not equivalent to random guesses