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 264264 ​trials, the touch therapists were correct 105105 times. Use a 0.050.05 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

Answer:

We conclude that the the touch therapists does not use a method equivalent to random guesses.

Yes, the results suggest that touch therapists are​ effective.

Step-by-step explanation:

We are given that in 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.

Among 264264 ​trials, the touch therapists were correct 105105 times.

Let p = proportion that touch therapists uses a random guess method.

Here, random guess means; p = 50%

So, Null Hypothesis, $H_0$ : p = 50%     {means that the touch therapists use a method equivalent to random guesses}

Alternate Hypothesis, $H_A$ : p $\neq$ 50%     {means that the touch therapists does not use a method equivalent to random guesses}

The test statistics that would be used here One-sample z proportion statistics;

                         T.S. =  $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$  ~ N(0,1)

where, $\hat p$  = sample proportion of touch therapists were correct = $\frac{105}{264}$ = 0.39

            n = sample of trials = 264

So, test statistics  =  $\frac{\frac{105}{264} -0.50}{\sqrt{\frac{\frac{105}{264}(1-\frac{105}{264})}{264} } }$  

                                =  -3.395

The value of z test statistics is -3.395.

Now, at 0.05 significance level the z table gives critical value of -1.96 and 1.96 for two-tailed test. Since our test statistics does not lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the the touch therapists does not use a method equivalent to random guesses.

Yes, the results suggest that touch therapists are​ effective.