Critical Thinking. In Exercises 17–28, use the data and confid...

Question

Critical Thinking. In Exercises 17–28, use the data and confidence level to construct a confidence interval estimate of p, then address the given question.

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?

Accepted Answer

Welcome back, everyone. A student conducted an experiment to test whether individuals could sense the outcome of a coin toss without seeing it. In each trial, the student flipped a fair coin and placed it under a cup. The participant then had to guess whether the coin showed heads or tails without any visual clues. The experiment was repeated 250 times, and participants guessed correctly 127 times. Given that the coin used was fair, what proportion of correct responses would be expected if the participants were just making random guesses? A says 0.25. B 0.40. C 0.50, and D 0.75. So here we have to understand that we're looking at an experiment with a sample size of 250, and we have 127 favorable outcomes. However, we're looking at the theoretical model where we have to predict the proportion, right? So let's recall that probability of an event A is the ratio between two numbers, M and N, where M is the number of favorable outcomes. And N is the number of total outcomes. So if we perform a single flip of a coin, and equals 2, right, because our sample space consists of heads and tails. So this gives us two possible outcomes. In a single toss, we can either be correct or incorrect, right? So M. is equal to 1. There's only one favorable outcome to be correct. So the probability in this context is going to be a 1 divided by 2. Which is 0.50. And therefore we can conclude that the correct answer to this problem corresponds to the answer choice C 0.50. Thank you for watching.

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Key Concepts

Proportion and Probability

Confidence Interval

Hypothesis Testing

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