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 = ) (round to two decimal places as needed.)

Explanation:

Step1: Calculate sample proportion $\hat{p}$

Sample proportion $\hat{p}=\frac{x}{n}$, where $x = 105$ (number of correct trials) and $n=246$ (total number of trials). So, $\hat{p}=\frac{105}{246}\approx0.427$.

Step2: Calculate the test - statistic $z$

The formula for the test - statistic in a one - sample proportion test is $z=\frac{\hat{p}-p}{\sqrt{\frac{p(1 - p)}{n}}}$.
Substitute $p = 0.5$ (from the null hypothesis $H_0:p = 0.5$), $\hat{p}\approx0.427$, and $n = 246$ into the formula.

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Answer:

$z\approx - 2.29$