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 354 trials, the touch therapists were correct 172 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? 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.
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 354 trials, the touch therapists were correct 172 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? 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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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Transcribed Image Text: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 354 trials, the touch therapists were correct 172 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?
(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.)
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.
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.
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