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 338 trials, the touch therapists were correct 159 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?

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

d) What do the results suggest about the success of touch therapists to select the correct hand by sensing energy field?

2.A random sample of 856 births in a state included 424 boys. Construct a 95% confidence interval estimate of the proportion of boys in all births. It is believed that armong all births, the proportion of boys is 0.512. Do these sample results provide strong evidence against that belief? Construct a 95% confidence interval estimate of the proportion of boys in all births.