Decision Errors
Each study tests whether a treatment really works — the null hypothesis says it does nothing; the alternative says it really works. Choose what's actually true, run many studies, and watch how often the test reaches the right verdict — and how often it makes a Type I or Type II error.
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Decision Errors — Help
Each study draws a sample of n patients, finds the success rate, and runs a one-proportion test of H₀: p = 0.50 (the treatment does nothing) against Hₐ: p > 0.50. A study can reach the right verdict or make one of two mistakes:
A note on wording: α is the discernibility level here, following the course text. Many books and exercise sets call the same number the significance level — they mean the same thing.
When Hₐ is true (it really works): rejecting H₀ detects the effect; failing to reject is a Type II error (a miss).
When H₀ is true (it does nothing): rejecting H₀ is a Type I error (a false alarm); failing to reject is the correct call. The false-alarm rate stays near α.
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