Question

A. Given that Emily used a coin toss to select either her right hand or her left​ hand, what proportion of correct responses would be expected if the touch therapists made random​ guesses?

​(Type an integer or a decimal. Do not​ round.)

b. Using​ Emily's sample​ results, what is the best point estimate of the​ therapists' success​ rate?

​(Round to three decimal places as​ needed.)

c. Using​ Emily's sample​ results, construct a 95​% confidence interval estimate of the proportion of correct responses made by touch therapists.

​(Round to three decimal places as​ needed.)

d. What do the results suggest about the ability of touch therapists to select the correct hand by sensing energy​ fields?

A.Since the confidence interval is not entirely above​ 0.5, there does not appear to be sufficient evidence that touch therapists can select the correct hand by sensing energy fields.

B.Since the lower confidence limit is below​ 0.5, there does not appear to be sufficient evidence that touch therapists can select the correct hand by sensing energy fields.

C.Since the confidence interval is not entirely below​ 0.5, there appears to be evidence that touch therapists can select the correct hand by sensing energy fields.

D.Since the upper confidence limit is above​ 0.5, there appears to be evidence that touch therapists can select the correct hand by sensing energy fields.

Answer 1

The expected proportion of correct responses from touch therapists making random guesses is 0.5. The best point estimate is calculated as the ratio of correct responses to total attempts, and a 95% confidence interval is built around this estimate. If the interval includes 0.5, there's no evidence that therapists can sense energy fields effectively.

Step-by-step explanation:

If Emily used a coin toss to select her right or left hand, the proportion of correct responses expected with random guesses would be 0.5, given that a coin has two sides and each side has an equal probability of being selected.

For part b, the best point estimate of the therapists' success rate is found by dividing the number of correct guesses by the total number of guesses. The formula is:
Point Estimate = (Number of correct responses) / (Total number of attempts).

To construct a 95% confidence interval in part c, use the formula:
Confidence Interval = Point estimate ± (Critical value) * (Standard error of the proportion)
where the standard error is calculated by SQRT[ (Point estimate * (1 - Point estimate)) / n ]. n represents the number of guesses made.

For part d, if the confidence interval includes 0.5, we cannot conclude the therapists can identify the correct hand better than random chance. Therefore, the correct interpretation would be option B: Since the lower confidence limit is below 0.5, there does not appear to be sufficient evidence that touch therapists can select the correct hand by sensing energy fields.