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Use the data and confidence level to construct a confidence interval estimate of $p,$ then address the given question.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 (basedon 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 proportionof correct responses made by touch therapists.

a. 0.5b. 0.439c. $0.363<p<0.516$d. If the touch therapists really had an ability to select the correcthand by sensing an energy field, their success rate would be significantly greater than 0.5 , but the sample success rate of0.439 and the confidence interval suggest that they do not have the ability to select the correct hand by scnsing an energy field.

Intro Stats / AP Statistics

Chapter 7

Estimating Parameters and Determining Sample Sizes

Section 1

Estimating a Population Proportion

Sampling and Data

Confidence Intervals

Experiment

University of North Carolina at Chapel Hill

Piedmont College

Idaho State University

Lectures

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04:39

Use the given sample data …

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When she was 9 years of ag…

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When she was nine years of…

When she was 9 years of a…

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In a science fair project,…

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Test the given claim. Iden…

03:10

Testing Claims About Propo…

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Use the data and confidenc…

01:50

Test of Touch Therapy Nine…

04:29

02:13

Nine-year-old Emily Rosa c…

03:56

04:06

03:35

Finding Confidence Interva…

03:50

now in part A. Okay, if the therapists are just guessing randomly. Okay. Given that Emily used a coin toss to select either her right hand or her left hand, what exactly would be the proportion of correct responses if the test therapists made random guesses? What is the probability of getting it right? It is 0.5, right. The probability is 50%. It's a 50 50 chance. So it's 0.5. Now, let us move on toe Part B in part B. We want to say what is the best point estimate of the therapists success rate? It has given that into 80 trials 1, 23 times they were correct. So it is going to be 1. 23 by 2. 81 23 by 2. 80. Right, 1 23 by 2. 18. So what is this? 123 divided by 280 This is 43% around. This is around 0.43924392 This is around 44%. Okay, this is the best point point estimate now moving on to part. See what is Park Si se now? Party wants us to construct a 99% confidence interval estimate off proportion off correct responses made by the touch therapists. So in this case, this is my peak cap. This is my peak cap. So what is going to be my cue cap? Que ca will be one minus speaker. Or I can write this as 0.56070 point 5607 Okay, now the formula for he is Z Alfa by route over P cap que capped by N N s to 80 anarchists. And what is myself? How I do it is going to be 2.57582 point 5758 Why? Because I want to construct a 99% confidence in my Alfa by two. In this case, alphabet to in this case is 0.5 So if I just do this calculation, this is going to be rude. Over 0.4392 multiplied by zero point 5607 divided by to 80 and after multiplied is about 2.575 point 5758 This is 0.763 Okay, let me illustrate the direct answer. 0.7 16. 0.763 Okay. And what is my pick up? 0.4392 Now, if I want to calculate the interval, my first lower limit will be pick up minus E, which is going to be 0.439 to minus 0.763 This is 0.3 69 0.36 to 9 less than p. And this is less than now. The addition of these two. What is the addition of these two? Plus 0.7 60. This is 0.51550 point +5155 Okay, Now, using the Emily sample results, we just had to construct an idea and person confidence interval to assume the proportion of correct response is made by the therapists. So this is going to be our answer. This is the confidence interval. We are 99% confident. Okay, We are 99% sure that the two proportion is going to lie between these two values. And this is our answer

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