Respuesta :
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, [tex]H_0[/tex] : p = 50% {means that the touch therapists use a method equivalent to random guesses}
Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 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. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of touch therapists were correct = [tex]\frac{105}{264}[/tex] = 0.39
n = sample of trials = 264
So, test statistics = [tex]\frac{\frac{105}{264} -0.50}{\sqrt{\frac{\frac{105}{264}(1-\frac{105}{264})}{264} } }[/tex]
= -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.
