12 a 12 a Sample Statistic Rejection Region Rejection Region Nonrejection

12 a 12 a sample statistic rejection region rejection

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1/2 a 1/2 a Sample Statistic Rejection Region Rejection Region Nonrejection Region Sampling Distribution 1 a Level of Confidence Rejection Regions (Two-Tailed Test) Sampling Distribution Observed sample statistic
H o Value Critical Value Critical Value 1/2 a 1/2 a Sample Statistic Rejection Region Rejection Region Nonrejection Region Sampling Distribution 1 a Level of Confidence Rejection Regions (Two-Tailed Test) Observed sample statistic
Decision Making Risks
Decision Results H 0 : Innocent Jury Trial Actual Situation Verdict Innocent Guilty Innocent Correct Error Guilty Error Correct H 0 Test Actual Situation Decision H 0 True H 0 False Accept H 0 1 a Type II Error ( b ) Reject H 0 Type I Error ( a ) Power (1 b )
Errors in Making Decision 1. Type I Error Reject true null hypothesis Has serious consequences Probability of Type I Error is a (alpha) Called level of significance 2. Type II Error Do not reject false null hypothesis Probability of Type II Error is b (beta)
Factors Affecting b 1. True value of population parameter Increases when difference with hypothesized parameter decreases 2. Significance level, a Increases when a decreases 3. Population standard deviation, Increases when increases 4. Sample size, n Increases when n decreases
Hypothesis Testing Steps
H 0 Testing Steps State H 0 State H a Choose a Choose n Choose test Set up critical values Collect data Compute test statistic Make statistical decision Express decision