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# ch21 - STAT 2023 Holbrook More About Tests 1 STAT 2023...

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Unformatted text preview: STAT 2023 - Holbrook More About Tests Chapter 21 21 - 1 STAT 2023 - Holbrook Observed Level of Significance: p­values (Next slide is same slide from Chapter 20.) 21 - 2 STAT 2023 - Holbrook p­Value 1. Probability of Obtaining a Test Statistic Probability More Extreme (≤ or ≥ ) than Actual More Sample Value Given H0 Is True Sample 2. Called Observed Level of Significance 2. Smallest Value of α H0 Can Be Rejected Smallest 3. Used to Make Rejection Decision 21 - 3 If p-Value < α, Reject H0 If If p-Value ≥ α, Do Not Reject H0 If STAT 2023 - Holbrook Significance Level (Recall that the Observed Level of Significance = p­value.) 21 - 4 STAT 2023 - Holbrook Level of Significance 1. Probability 2. Defines Unlikely Values of Sample Statistic (i.e. Defines test statistic in step 2 of hypothesis testing) if Null Hypothesis Is True Null Called Rejection Region of Sampling Distribution 3. Designated α (alpha) Designated (alpha) Typical Values Are .01, .05, .10 4. Selected by Researcher at Start 5. Specifically: Probability of a Type I Error 21 - 5 STAT 2023 - Holbrook Errors in Making Decision 1. Type I Error Reject a True Null Hypothesis Has Serious Consequences Probability of Type I Error Is α (Alpha) Probability (Alpha) Called Level of Significance 2. Type II Error 21 - 6 Fail to Reject a False Null Hypothesis Probability of Type II Error Is β (Beta) Probability (Beta) May also have serious consequences Decision Results STAT 2023 - Holbrook H0: Innocent Jury Trial H0 Test Actual Situation Verdict Innocent Guilty Decision H0 True Innocent Correct Guilty 21 - 7 Actual Situation Error Error Do Not Reject H0 Correct Reject H0 1-α H0 False Type II Error (β ) Type I Power Error (α) (1 - β ) STAT 2023 - Holbrook Decision Results H0: Innocent Jury Trial Actual Situation Verdict 21 - 8 Actual Situation Innocent Guilty Decision H0 True Innocent Correct Guilty H0 Test Error Error Correct Accept H0 Reject H0 1-α H0 False Type II Error (β) Type I Power Error (α (1 - ) ) β STAT 2023 - Holbrook α & β Have an Inverse Relationship You can’t reduce both errors simultaneously! β α 21 - 9 Factors Affecting β STAT 2023 - Holbrook (optional) (optional) 1. True Value of Population Parameter Increases When Difference With Hypothesized Increases Parameter Decreases Parameter 2. Significance Level, α Significance Increases When α Decreases Increases Decreases 3. Population Standard Deviation, σ Population Increases When σ Increases Increases 4. Sample Size, n 4. Sample 21 - 10 10 Increases When n Decreases Increases STAT 2023 - Holbrook Power of Test (optional) 1. Probability of Rejecting False H0 Correct Decision 2. Designated 1 - β Designated 3. Used in Determining Test Adequacy 21 - 11 11 STAT 2023 - Holbrook Examples 21 - 12 12 STAT 2023 - Holbrook One Proportion Z Test Example Is drug use running rampant? Is 200 students at SFCC were 200 asked if they have ever smoked marijuana and 140 responded 140 yes. Is the population proportion of SFCC students who have ever smoked marijuana more than 60% ? Set up the null and 60% alternative hypothesis. Define a type I and type II error. Which is more severe? more 21 - 13 13 STAT 2023 - Holbrook One Proportion Z Test Solution H0: p = .6 Ha: p > .6 n = 200 Test Statistic: P-value: P-value: Decision: Decision: Conclusion: 21 - 14 14 STAT 2023 - Holbrook One Proportion Z Test Solution 1. Type I Error Reject a True Null Hypothesis Saying that the population proportion of Saying SFCC students who have smoked marijuana IS > .60, when it really IS NOT. IS IS 2. Type II Error 21 - 15 15 Fail to Reject a False Null Hypothesis Saying that the population proportion of Saying SFCC students who have smoked marijuana IS NOT > .60, when it really IS. IS IS STAT 2023 - Holbrook Solution continued: Which is more severe? 1. Type I Error Falsely claiming that there might be a Falsely problem with marijuana use (drug use is running rampant!). running 2. Type II Error 21 - 16 16 Falsely claiming that there isn’t a problem Falsely with marijuana use (when there might be!). be!). STAT 2023 - Holbrook One­Proportion Z Test Example The present packaging system The produces 10% defective 10% cereal boxes. Using a new system, a random sample of 200 boxes had 11 defects. 200 11 Does the new system produce fewer defects? Set up the null fewer and alternative hypothesis. Define a type I and type II error. Which is more severe? error. 21 - 17 17 STAT 2023 - Holbrook One­Proportion Z Test Solution H0: p = .10 Ha: p < .10 n = 200 Test Statistic: P-Value: P-Value: Decision: Decision: Conclusion: 21 - 18 18 STAT 2023 - Holbrook One Proportion Z Test Solution 1. Type I Error Reject a True Null Hypothesis Saying that the population proportion of Saying defective cereal boxes IS < .10, when it IS really IS NOT. IS 2. Type II Error 21 - 19 19 Fail to Reject a False Null Hypothesis Saying that the population proportion of Saying defective cereal boxes IS NOT < .10, IS when it really IS. IS STAT 2023 - Holbrook Solution continued: Which is more severe? 1. Type I Error Implement the new procedure when we Implement shouldn’t have. shouldn’t Results in unnecessary use of time and Results money. money. 2. Type II Error 21 - 20 20 Not implementing the new procedure Not when we should have. when Results in using the ineffective old Results procedure. procedure. End of Chapter Any blank slides that follow are blank intentionally. ...
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