Question

13.

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 352 ​trials, the touch therapists were correct 166 times. Complete parts​ (a) through​ (d).

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

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

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

Answer 1

Answer:

a)

Given,

sample proportion p^ = x/n = 166/352 = 0.4716

p = 0.5

Expected number = np = 352*0.5 = 176

Proportion of correct responses = 176/352 = 0.5

b)

Success rate = 166/352 = 0.4716

c)

Confidence interval = p^ +/- z*sqrt(p^(1-p^)/n)

substitute values

= 0.4716 +/- 1.65*sqrt(0.4716(1-0.4716)/352)

= 0.4716 +/- 0.0439

= (0.4277 , 0.5155)

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.