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?

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

Step-by-step 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                    

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