Question

when she was 9 years of age, a 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 246 trials, the touch therapists were correct 105 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? let p denote the population proportion of correct hand selections by touch therapists. identify the null and alternative hypotheses to test the claim that touch therapists use a method equivalent to random guesses. ( h_0: p = 0.5 ) ( h_1: p
eq 0.5 ) (type integers or decimals. do not round.) identify the test statistic. ( z = -2.28 ) (round to two decimal places as needed.) identify the p - value. p - value ( = 0.022 ) (round to three decimal places as needed.) state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. address whether the results suggest that touch therapists are effective. the null hypothesis. there sufficient evidence to the claim that touch therapists use a method equivalent to random guesses. the results that touch therapists are effective.

Explanation:

Step1: Compare P - value and significance level

We are given a significance level \(\alpha = 0.10\) and a P - value \(P=0.022\).
Since \(P = 0.022<\alpha=0.10\).

Step2: Make decision about null hypothesis

When \(P<\alpha\), we reject the null hypothesis \(H_0:p = 0.5\).

Step3: Draw conclusion about the claim

Since we reject \(H_0\), there is sufficient evidence to reject the claim that touch therapists use a method equivalent to random guesses.
Since we reject the claim that \(p = 0.5\) (random guess), and the sample proportion \(\hat{p}=\frac{105}{246}\approx0.427\) (less than \(0.5\)), the results do not suggest that touch therapists are effective.

Answer:

Reject the null hypothesis. There is sufficient evidence to reject the claim that touch therapists use a method equivalent to random guesses. The results do not suggest that touch therapists are effective.