17. Births A random sample of 860 births in New York State included 426 boys. Construct a 95%
confidence interval estimate of the proportion of boys in all births. It is believed that among all births,
the proportion of boys is 0.512. Do these sample results provide strong evidence against that belief?
19. Tennis Challenges In a recent U. S. Open tennis tournament, women playing single
matches used challenges on 137 calls made by the line judges. Among those challenges, 3
were found to be successful with the call overturned.
a. Construct a 99% confidence interval for the percentage of successful challenges.
b. Compare the result from part (a) to this 99% confidence interval for the percentage of successful challenges made by the men playing singles matches: 28.7% <p< 44.7%. Does
appear that either gender is more successful than the other?
21. Touch Therapy When she was 9 years of age, Emily Rosa did a science fair 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 280 trials, the touch therapists were correct 123 times (based
on data in "A Close Look at Therapeutic Touch," Journal of the American Medical Association,
Vol. 279, No. 13).
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 99% confidence interval estimate of the proportion
of correct responses made by touch therapists.
d. What do the results suggest about the ability of touch therapists to select the correct hand by
sensing an energy field?