Question

In a science fair​ project, Emily conducted an 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​ Emily's hand without seeing it and without touching it. Among

322322

​trials, the touch therapists were correct

156156

times. Complete parts​ (a) through​ (d).

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?

nothing

​(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?

nothing

​(Round to three decimal places as​ needed.)c. Using​ Emily's sample​ results,

construct

a

9595​%

confidence interval estimate of the proportion of correct responses made by touch therapists.

nothingless than<pless than<nothing

​(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 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.

B.

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.

C.

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.

Answer 1

a) proportion of correct responses would be expected if the touch therapists made random​ guesses =np=322*0.5=161

b) best point estimate of the​ therapists' success​ rate =156/322=0.484

c)

95​% confidence interval estimate of the proportion of correct responses made by touch therapists =0.429 , 0.539

( please try 0.430 , 0.539 if this comes wrong)

d)

C.

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.