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 287 ​trials, the touch therapists were correct 133 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?

c. Using​ Emily's sample​ results,construct a 95% confidence interval estimate of the proportion of correct responses made by touch therapists.

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

Answer 1

(a)

Since coin is fair so probability of getting a head or tail is 0.5 therefore proportion of correct responses would be expected if the touch therapists made random​ guesses is 0.50.

(b)

The best point estimate of the​ therapists' success​ rate is

(c)