Please show all work done to derive answer. Thank You. Testing Claims about Proo

Question

Please show all work done to derive answer. Thank You. Testing Claims about Proortion.test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic,P-vAlue or critical value(s), conclusion about the null hypothesis and final conclusion that addresses the original claim. Use the Pvaluemethod.use the normal distribution as an approximation to the binomial distribution . Touch Therapy. When she's 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, 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). Use a 0.10 significance level to test the claim that touch therapists use a method equivalent to random guesses. Do the results suggest that touch therapists are effective? Please show all work done to derive answer. Thank You. Testing Claims about Proortion.test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic,P-vAlue or critical value(s), conclusion about the null hypothesis and final conclusion that addresses the original claim. Use the Pvaluemethod.use the normal distribution as an approximation to the binomial distribution . Touch Therapy. When she's 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, 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). Use a 0.10 significance level to test the claim that touch therapists use a method equivalent to random guesses. Do the results suggest that touch therapists are effective? Testing Claims about Proortion.test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic,P-vAlue or critical value(s), conclusion about the null hypothesis and final conclusion that addresses the original claim. Use the Pvaluemethod.use the normal distribution as an approximation to the binomial distribution . Touch Therapy. When she's 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, 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). Use a 0.10 significance level to test the claim that touch therapists use a method equivalent to random guesses. Do the results suggest that touch therapists are effective?

Explanation / Answer

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.5
Ha:   p   >   0.5
As we see, the hypothesized po =   0.5      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.439285714      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.029880715      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -2.031888636      
          
As this is a    1   tailed test, then, getting the critical value
          
zcrit = 1.28

As z < 1.28, we fail to reject Ho.

There is no significant evidence that the touch therapists are more effective than someone who is just guessing. [CONCLUSION]

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Actually, in the first place, there is no sense to test it at all as 123/280 means they got it correctly less than half of the time, but we tested it anyway.

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