 In a Hypothesis test there are two possible mistakes Null Hypothesis TrueFalse Result of Hypothesis Test Reject Fail to Reject Correct Type I Error.

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 In a Hypothesis test there are two possible mistakes Null Hypothesis TrueFalse Result of Hypothesis Test Reject Fail to Reject Correct Type I Error Type II Error

 In our system of courts Defendant InnocentGuilty Jury decision Convict Don’t Convict Correct Type I Error Type II Error

 A Type I error happens when we reject a true null hypothesis ◦ we convict an innocent person  A Type II error happens when we fail to reject a false hypothesis ◦ we set free a guilty person

Sunday School teachers Upstanding Citizens Jailed Criminals The Usual Suspects

Appearance of Guilt Standard of Proof Not Guilty VerdictGuilty Verdict Type I Error

Innocent Suspects Dumb Criminals with incompetent lawyers caught red handed Standard of Proof Not Guilty VerdictGuilty Verdict

Type I Error Type II Error Standard of Proof Not Guilty VerdictGuilty Verdict Innocent Suspects Smart Criminals with top notch lawyers

 Alpha(α) = Probability of a Type I error.  Beta(β) = Probability of a Type II error.  Power of the test = 1 – β  Power is the probability of rejecting the null hypothesis if it were actually false.  Beta and power can only be calculated if we knew the actual hypothesis.

 If we decrease alpha, beta is increased and power is decreased  If we increase alpha, beta is decreased and power is increased  If we increase the sample size, alpha is decreased, beta is decreased and power is increased.