Use the sign test for the claim involving nominal data. Touch Therapy? At the age of 9, Emily Rosa 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 and wrong the other times (based on data in “A Close Look at Therapeutic Touch,” Journal of the American Medical Association,? Vol. 279, No. 13). Use a 0.01 significance level to test the claim that the touch therapists make their selections with a method equivalent to random guesses. Based on the results, does it appear that therapists are effective at identifying the correct hand?
Solution 15BSC Step 1 Let us denote ‘p’ as the proportion of touch therapists were correct i.e., Proportion of touch therapists were correct (p) = 1 = 0.5. 2 By using = 0.01 level of significance to test the claim that the touch therapists make their selections with a method equivalent to random guesses. Among 280 trials, the touch therapists were correct 123 times and wrong the other times The Hypotheses can be expressed as H0 p = 0.5 (proportion of touch therapists were correct = 0.5) H : p > 0.5 (proportion of touch therapists were incorrect) 1 Step 2 Let us denote negative sign (-) for touch therapists were incorrect and positive sign (+) for touch therapists were correct, we have 157 negative signs and 123 positive signs. Now we need to determine whether 52 girls are low to be significant, hence we make use of left tailed test. Positive signs = 123 Negative signs = 157 Number of ties = 0 Now, the Test Statistic is the less frequent sign i.e., positive sign = 123 Therefore, x = 157 is the required value of test statistic. Hence for sign test the required sample size used is 280 i.e., n = 123 + 157 = 280 which is greater than 25 (n 25).