QQuestionStatistics
QuestionStatistics
A 9 -year-old girl conducted a science fair experiment to test whether professional touch therapists could sense her energy field. She flipped a coin to select either her right hand or left hand and asked the therapists to identify the chosen hand by placing their hand just below hers, without seeing it and without touching it. Among 282 trials, the touch therapists were correct 117 times.
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?
What is the test statistic for this hypothesis test? Round your answer to two decimal places.
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Answer
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Step 1:I'll solve this hypothesis test step by step using the appropriate statistical method.
Step 2:: Define the Hypotheses
- Null Hypothesis ($$H_{0}$$): The touch therapists are guessing randomly (probability of success = 0.5)
- Alternative Hypothesis (H_{1}): The touch therapists are not guessing randomly (probability ≠ 0.5)
Step 3:: Calculate Test Parameters
- Hypothesized probability of success: $$p_{0} = 0.5
- Number of correct guesses: k = 117
Step 4:: Select Test Statistic
For this scenario, we'll use the z-test for proportions.
Step 5:: Calculate Sample Proportion
\hat{p} = \frac{k}{n} = \frac{117}{282} = 0.4150
Step 6:: Calculate Standard Error
SE = \sqrt{\frac{p_{0}(1-p_{0})}{n}} = \sqrt{\frac{0.5(1-0.5)}{282}} = 0.0297
Step 7:: Calculate Z-Statistic
z = \frac{\hat{p} - p_{0}}{SE} = \frac{0.4150 - 0.5}{0.0297} = -2.36
Final Answer
The test statistic is - 2.36 (rounded to two decimal places).
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