91影视

In a sample of 280 trials, the touch therapists were correct 123 times.

a.

There are two possible outcomes to select: right hand or left hand

Since one of the two hands has the coin, the number of correct outcomes is equal to 1.

The proportion of correct responses is computed below:

$$\begin{gathered} p=\frac{\text{Number}\text{of}\text{correct}\text{responses}}{\text{Total}\text{number}\text{of}\text{responses}} \\ =\frac{1}{2} \\ =0.5 \end{gathered}$$

Thus, the proportion of correct responses is equal to 0.5.

b.

The best point estimate of the therapists鈥� success rate is the sample proportion of correct guesses made by the therapists.

Let x be the number of correct responses.

Let n be the sample size.

$$\begin{gathered} \hat{p}=\frac{x}{n} \\ =\frac{123}{280} \\ =0.439 \end{gathered}$$

The best point estimate of therapists鈥� success rate is 0.439.

c.

The formula for the confidence interval is given as follows:

$CI=\hat{p}-E<p<\hat{p}+E$

The right-tailed critical value of $z_{\frac{伪}{2}}$when $伪=0.01$is equal to 2.5758.

The value of the margin of error (E) is computed below:

$$\begin{gathered} E=z_{\frac{伪}{2}}脳\sqrt{\frac{\hat{p}\hat{q}}{n}} \\ =z_{\frac{0.01}{2}}脳\sqrt{\frac{0.44脳0.56}{280}} \\ =2.5758脳\sqrt{\frac{0.44脳0.56}{280}} \\ =0.0764 \end{gathered}$$

Substituting the required values, the following confidence interval is obtained:

$$\begin{gathered} \hat{p}-E<p<\hat{p}+E \\ 0.439-0.0764<p<0.439+0.0764 \\ 0.363<p<0.516 \end{gathered}$$

Thus, the 99% confidence interval estimate of the proportion of correct responses is equal to (0.36, 0.516).

d.

The sample proportion of correct guesses made by the therapists is equal to 0.439, which is even lower than 0.5.

Moreover, the confidence interval suggests that the proportion of correct responses is quite low.

Therefore, touch therapists are not very efficient in their ability to sense the energy field.