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 329 trials, the touch therapists were correct 154 times.
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?
b. Using Emily's sample results, what is the best point estimate of the therapists' success rate?
c. Using Emilys sample results, construct a 90% confidence interval estimate of the proportion of correct responses made by touch therapists.