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 358 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. Round to three decimal places as needed - ?&lt;p&lt;?

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&#039;s hand without seeing it and without touching it. Among 358 ​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&#039;s sample​ results, what is the best point estimate of the​ therapists&#039; success​ rate? ​(Round to three decimal places as​ needed.) c) Using​ Emily&#039;s sample​ results, construct a 90​% confidence interval estimate of the proportion of correct responses made by touch therapists. Round to three decimal places as​ needed - ?&amp;lt;p&amp;lt;?

Theodore Schwartz · Accepted Answer

Step 1 Given: n=358 x=172 a) The proportion of correct responses is obtained as below: p^=xn =172358 =0.480 Thus, the proportion of correct responses is 0.480. Step 2 b) The best point estimate of the​ therapists&#039; success​ rate is obtained as below: Point estimate of p=p^ =0.480 Thus, the best point estimate of the​ therapists&#039; success​ rate is 0.480. c) From the Standard Normal Table, the value of z× for 90% level is 1.645. The 90​% confidence interval estimate of the proportion of correct responses made by touch therapist is obtained as below: sample statistic ±z×SE=p^±z×p^(1−p^)n =0.480±1.645×0.480×0.520358 =0.480±(1.645×0.0264) =0.480±0.0434 =(0.437, 0.523) Thus, the 90​% confidence interval estimate of the proportion of correct responses made by touch therapist is 0.437&amp;lt;p&amp;lt;0.523.

In a science fair project, Emily conducted an experiment in which she tested pr

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