**Hypothesis Testing: Identifying Conclusions** To determine the outcome of a hypothesis test, use the P-value calculated for the test. This will help us decide whether to reject or fail to reject the null hypothesis (H₀). **Identify the conclusion for this hypothesis test:** 1. **Option A: Reject H₀.** - There is sufficient evidence to warrant rejection of the claim that touch therapists use a method equivalent to random guesses. 2. **Option B: Fail to reject H₀.** - There is sufficient evidence to warrant rejection of the claim that touch therapists use a method equivalent to random guesses. 3. **Option C: Fail to reject H₀.** - There is not sufficient evidence to warrant rejection of the claim that touch therapists use a method equivalent to random guesses. 4. **Option D: Reject H₀.** - There is not sufficient evidence to warrant rejection of the claim that touch therapists use a method equivalent to random guesses. **Question:** Do the results suggest that touch therapists use a method equivalent to random guesses, or do they suggest that touch therapists use a method that is effective? Use the provided P-value to round to two decimal places if necessary, and make a selection for the appropriate conclusion. **Hypothesis Testing: A Study on Touch Therapy** **Experiment Overview:** A 9-year-old girl conducted a science fair experiment to test the ability of professional touch therapists to sense her energy field. In the experiment, the therapists were asked to identify which of her hands was just under theirs, without seeing. To ensure fairness, the girl flipped a coin to randomly select either her left or right hand for placement. Across 271 trials, the therapists correctly identified the hand 114 times. **Research Question:** Does the performance of the touch therapists indicate effectiveness beyond random guessing? This test will use a significance level of 0.10. **Steps for Hypothesis Testing:** 1. **Identify the Null and Alternative Hypotheses:** - **Option A:** - \( H_0 \): \( p = 0.5 \) - \( H_1 \): \( p < 0.5 \) - **Option B:** - \( H_0 \): \( p = 0.5 \) - \( H_1 \): \( p > 0.5 \) - **Option C:** - \( H_0 \): \( p = 0.5 \) - \( H_1 \): \( p \neq 0.5 \) - **Option D:** - \( H_0 \): \( p = 0.5 \) - \( H_1 \): \( p \neq 0.5 \) 2. **Calculate the Test Statistic:** - Compute the test statistic for the hypothesis test. (Round to two decimal places.) 3. **Determine the P-value:** - Identify the P-value for this hypothesis test. (Round to three decimal places as needed.) 4. **Conclusion:** - Identify the conclusion for this hypothesis test based on the results and the significance level. Through this structured process, you will be able to draw a conclusion on whether the therapists can successfully identify the girl's hand location beyond random chance.