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 327 ​trials, the touch therapists were correct 158 times. Complete parts​ (a) through​ (d).

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.

less than <p less than< (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 below​ 0.5, there appears to be evidence that touch therapists can select the correct hand by sensing energy fields.

D.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

The statistical software output for this problem is:

Hence,

a) Expected proportion of correct guesses = 0.50

b) Best point estimate = 158/327 = 0.483

c) 95% confidence interval:

0.429 < p < 0.537

d) 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. Option D is correct.