Type I and Type II Errors, Power, and Significance
A decision-and-workflow guide for Type I error, Type II error, and power, covering method selection, conditions, mathematics, calculator evidence, and contextual reporting.
Method at a Glance: Type 1 And Type 2 Error
Type I error rejects a true null with probability alpha, Type II error fails to reject a false null at a specified alternative, and power equals one minus beta.
Procedure Workflow
- Identify the data structure and parameter before selecting type 1 and type 2 error; the name of a calculator menu is not method evidence.
- State the hypotheses or estimation target for type 1 and type 2 error using population notation and the order defined by the question.
- Verify the design, independence, and approximation conditions that specifically justify type 1 and type 2 error rather than reciting every condition learned in the course.
- Compute the statistic, standard error, interval, or p-value for type 1 and type 2 error with defined symbols, guard digits, and an independent arithmetic check.
- Interpret type 1 and type 2 error in the population and units named by the problem, then limit causation and generalization to what the collection design supports.
Procedure Formulas and Notation
Type I error probability
Type I error probability in Type 1 And Type 2 Error: Define the event or random variable first; complements, conditioning, and trial assumptions determine which probability expression applies.
Statistical power
Statistical power in Type 1 And Type 2 Error: This expression belongs specifically to Type I error, Type II error, and power; define every symbol and apply the scope rule for contextual consequences, alpha, sample size, effect size, and tradeoffs before calculation.
Type I error
Decision
For Type I error in type 1 and type 2 error, For a test in a school library checkout study, state Type I and Type II errors in context and explain how sample size affects power.
Type I error result in type 1 and type 2 error: Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size.
Interpretation and validity
Type I error interpretation for type 1 and type 2 error: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim.
Condition evidence for type 1 and type 2 error and Type I error: Each error must name the actual population state and the decision the procedure makes.
Type II error
Decision
For Type II error in type 1 and type 2 error, For a test in a campus dining survey, state Type I and Type II errors in context and explain how sample size affects power.
Type II error result in type 1 and type 2 error: Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size.
Interpretation and validity
Type II error interpretation for type 1 and type 2 error: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim.
Condition evidence for type 1 and type 2 error and Type II error: Each error must name the actual population state and the decision the procedure makes.
Contextual statements
Decision
For Contextual statements in type 1 and type 2 error, For a test in a quality-control inspection, state Type I and Type II errors in context and explain how sample size affects power.
Contextual statements result in type 1 and type 2 error: Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size.
Interpretation and validity
Contextual statements interpretation for type 1 and type 2 error: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim.
Condition evidence for type 1 and type 2 error and Contextual statements: Each error must name the actual population state and the decision the procedure makes.
Power
Decision
For Power in type 1 and type 2 error, For a test in a tutoring-program evaluation, state Type I and Type II errors in context and explain how sample size affects power.
Power result in type 1 and type 2 error: Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size.
Interpretation and validity
Power interpretation for type 1 and type 2 error: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim.
Condition evidence for type 1 and type 2 error and Power: Each error must name the actual population state and the decision the procedure makes.
Factors affecting power
Decision
For Factors affecting power in type 1 and type 2 error, For a test in a tutoring-program evaluation, state Type I and Type II errors in context and explain how sample size affects power.
Factors affecting power result in type 1 and type 2 error: Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size.
Interpretation and validity
Factors affecting power interpretation for type 1 and type 2 error: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim.
Condition evidence for type 1 and type 2 error and Factors affecting power: Each error must name the actual population state and the decision the procedure makes.
α trade-offs
Decision
For α trade-offs in type 1 and type 2 error, For a test in a campus dining survey, state Type I and Type II errors in context and explain how sample size affects power.
α trade-offs result in type 1 and type 2 error: Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size.
Interpretation and validity
α trade-offs interpretation for type 1 and type 2 error: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim.
Condition evidence for type 1 and type 2 error and α trade-offs: Each error must name the actual population state and the decision the procedure makes.
Sample size
Decision
For Sample size in type 1 and type 2 error, For a test in a recycling-behavior survey, state Type I and Type II errors in context and explain how sample size affects power.
Sample size result in type 1 and type 2 error: Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size.
Interpretation and validity
Sample size interpretation for type 1 and type 2 error: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim.
Condition evidence for type 1 and type 2 error and Sample size: Each error must name the actual population state and the decision the procedure makes.
Practice
Decision
For Practice in type 1 and type 2 error, For a test in a greenhouse germination experiment, state Type I and Type II errors in context and explain how sample size affects power.
Practice result in type 1 and type 2 error: Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size.
Interpretation and validity
Practice interpretation for type 1 and type 2 error: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim.
Condition evidence for type 1 and type 2 error and Practice: Each error must name the actual population state and the decision the procedure makes.
Procedure Practice and Full Solutions
Every question in Type I and Type II Errors, Power, and Significance is newly written from the revised framework and the logic visible in public College Board materials. Constructed numerical settings are identified as instructional scenarios and are never represented as measurements from a real population. No released or secure question wording is reproduced.
Easy Practice
Easy 1: α trade-offs
Question P63-Easy-1. For a test in a classroom memory study, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Easy-1. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Easy 2: Sample size
Question P63-Easy-2. For a test in a greenhouse germination experiment, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Easy-2. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Easy 3: Practice
Question P63-Easy-3. For a test in a manufacturing fill-volume check, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Easy-3. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Easy 4: Type I error
Question P63-Easy-4. For a test in a recycling-behavior survey, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Easy-4. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Easy 5: Type II error
Question P63-Easy-5. For a test in a campus dining survey, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Easy-5. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Easy 6: Contextual statements
Question P63-Easy-6. For a test in a commuter route study, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Easy-6. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Easy 7: Power
Question P63-Easy-7. For a test in a public-parks visitor survey, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Easy-7. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Easy 8: Factors affecting power
Question P63-Easy-8. For a test in a seedling-growth comparison, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Easy-8. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Easy 9: α trade-offs
Question P63-Easy-9. For a test in a city bus arrival investigation, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Easy-9. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Easy 10: Sample size
Question P63-Easy-10. For a test in a campus dining survey, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Easy-10. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Easy 11: Practice
Question P63-Easy-11. For a test in a reading-speed investigation, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Easy-11. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Easy 12: Type I error
Question P63-Easy-12. For a test in a greenhouse germination experiment, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Easy-12. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Easy 13: Type II error
Question P63-Easy-13. For a test in a recycling-behavior survey, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Easy-13. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Easy 14: Contextual statements
Question P63-Easy-14. For a test in a seedling-growth comparison, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Easy-14. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Tough Practice
Tough 1: Practice
Question P63-Tough-1. For a test in a reading-speed investigation, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Tough-1. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Tough 2: Type I error
Question P63-Tough-2. For a test in an online-course completion sample, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Tough-2. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Tough 3: Type II error
Question P63-Tough-3. For a test in a school library checkout study, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Tough-3. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Tough 4: Contextual statements
Question P63-Tough-4. For a test in a tutoring-program evaluation, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Tough-4. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Tough 5: Power
Question P63-Tough-5. For a test in a commuter route study, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Tough-5. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Tough 6: Factors affecting power
Question P63-Tough-6. For a test in a school library checkout study, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Tough-6. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Tough 7: α trade-offs
Question P63-Tough-7. For a test in a campus dining survey, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Tough-7. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Tough 8: Sample size
Question P63-Tough-8. For a test in a public-parks visitor survey, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Tough-8. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Tough 9: Practice
Question P63-Tough-9. For a test in a campus dining survey, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Tough-9. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Tough 10: Type I error
Question P63-Tough-10. For a test in a manufacturing fill-volume check, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Tough-10. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Tough 11: Type II error
Question P63-Tough-11. For a test in an online-course completion sample, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Tough-11. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Tough 12: Contextual statements
Question P63-Tough-12. For a test in a school library checkout study, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Tough-12. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Tough 13: Power
Question P63-Tough-13. For a test in a recycling-behavior survey, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Tough-13. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Tough 14: Factors affecting power
Question P63-Tough-14. For a test in an online-course completion sample, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Tough-14. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Toughest Practice
Toughest 1: Factors affecting power
Question P63-Toughest-1. For a test in a website response-time study, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Toughest-1. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Toughest 2: α trade-offs
Question P63-Toughest-2. For a test in a package-delivery sample, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Toughest-2. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Toughest 3: Sample size
Question P63-Toughest-3. For a test in a quality-control inspection, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Toughest-3. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Toughest 4: Practice
Question P63-Toughest-4. For a test in a quality-control inspection, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Toughest-4. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Toughest 5: Type I error
Question P63-Toughest-5. For a test in a public-parks visitor survey, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Toughest-5. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Toughest 6: Type II error
Question P63-Toughest-6. For a test in a city bus arrival investigation, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Toughest-6. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Toughest 7: Contextual statements
Question P63-Toughest-7. For a test in a greenhouse germination experiment, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Toughest-7. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Toughest 8: Power
Question P63-Toughest-8. For a test in a seedling-growth comparison, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Toughest-8. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Toughest 9: Factors affecting power
Question P63-Toughest-9. For a test in a website response-time study, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Toughest-9. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Toughest 10: α trade-offs
Question P63-Toughest-10. For a test in a commuter route study, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Toughest-10. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Toughest 11: Sample size
Question P63-Toughest-11. For a test in a greenhouse germination experiment, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Toughest-11. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Toughest 12: Practice
Question P63-Toughest-12. For a test in a greenhouse germination experiment, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Toughest-12. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Toughest 13: Type I error
Question P63-Toughest-13. For a test in a recycling-behavior survey, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Toughest-13. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
Toughest 14: Type II error
Question P63-Toughest-14. For a test in a quality-control inspection, state Type I and Type II errors in context and explain how sample size affects power.
Worked solution and validity check
Worked solution P63-Toughest-14. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Each error must name the actual population state and the decision the procedure makes. Error to reject: Do not describe Type II error as accepting H0; the correct decision language is fail to reject.
AP Response and Publication Checklist
| Audit point | Required evidence for type 1 and type 2 error |
|---|---|
| Scope | Power is computed under a specified alternative value, not under H0. |
| Method or source | Type I error rejects a true null with probability alpha, Type II error fails to reject a false null at a specified alternative, and power equals one minus beta. |
| Calculation | If alpha is 0.05, the procedure is calibrated so the Type I error probability is 0.05 when the null model and conditions hold. Power is . |
| Interpretation | Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. |
| Validity | Each error must name the actual population state and the decision the procedure makes. |
| Correction | Do not describe Type II error as accepting H0; the correct decision language is fail to reject. |
Frequently Asked Questions
How does type i error work in type 1 and type 2 error?
Answer for type 1 and type 2 error and Type I error. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. The required validity evidence is: Each error must name the actual population state and the decision the procedure makes.
How does type ii error work in type 1 and type 2 error?
Answer for type 1 and type 2 error and Type II error. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. The required validity evidence is: Each error must name the actual population state and the decision the procedure makes.
How does contextual statements work in type 1 and type 2 error?
Answer for type 1 and type 2 error and Contextual statements. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. The required validity evidence is: Each error must name the actual population state and the decision the procedure makes.
How does power work in type 1 and type 2 error?
Answer for type 1 and type 2 error and Power. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. The required validity evidence is: Each error must name the actual population state and the decision the procedure makes.
How does factors affecting power work in type 1 and type 2 error?
Answer for type 1 and type 2 error and Factors affecting power. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. The required validity evidence is: Each error must name the actual population state and the decision the procedure makes.
How does α trade-offs work in type 1 and type 2 error?
Answer for type 1 and type 2 error and α trade-offs. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. The required validity evidence is: Each error must name the actual population state and the decision the procedure makes.
How does power of hypothesis test connect to Type 1 And Type 2 Error?
power of hypothesis test within type 1 and type 2 error. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. For Type I error, the controlling scope is: Power is computed under a specified alternative value, not under H0.
How does hypothesis testing type i and type ii errors connect to Type 1 And Type 2 Error?
hypothesis testing type i and type ii errors within type 1 and type 2 error. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. For Type II error, the controlling scope is: Power is computed under a specified alternative value, not under H0.
How does power of the hypothesis test connect to Type 1 And Type 2 Error?
power of the hypothesis test within type 1 and type 2 error. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. For Contextual statements, the controlling scope is: Power is computed under a specified alternative value, not under H0.
How does type i and type ii errors in hypothesis testing connect to Type 1 And Type 2 Error?
type i and type ii errors in hypothesis testing within type 1 and type 2 error. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. For Power, the controlling scope is: Power is computed under a specified alternative value, not under H0.
How does type 1 and type 2 errors in hypothesis testing connect to Type 1 And Type 2 Error?
type 1 and type 2 errors in hypothesis testing within type 1 and type 2 error. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. For Factors affecting power, the controlling scope is: Power is computed under a specified alternative value, not under H0.
How does hypothesis testing type 1 and 2 errors connect to Type 1 And Type 2 Error?
hypothesis testing type 1 and 2 errors within type 1 and type 2 error. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. For α trade-offs, the controlling scope is: Power is computed under a specified alternative value, not under H0.
How does power of a hypothesis test connect to Type 1 And Type 2 Error?
power of a hypothesis test within type 1 and type 2 error. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. For Sample size, the controlling scope is: Power is computed under a specified alternative value, not under H0.
How does what is the power of a hypothesis test connect to Type 1 And Type 2 Error?
what is the power of a hypothesis test within type 1 and type 2 error. Type I rejects a true null; Type II fails to reject a false null. Larger n usually increases power for a fixed alpha and effect size. Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. For Practice, the controlling scope is: Power is computed under a specified alternative value, not under H0.
Sources
Administrative and curricular statements in Type I and Type II Errors, Power, and Significance were checked on July 18, 2026. The linked College Board pages control any later policy change; all instructional datasets in original questions are explicitly constructed rather than attributed to a real study.
Type 1 And Type 2 Error Conclusion
Type I error rejects a true null with probability alpha, Type II error fails to reject a false null at a specified alternative, and power equals one minus beta. Mastery of type 1 and type 2 error therefore requires the exact evidence, mathematics, interpretation, and scope developed in this guide, while preserving this boundary: Power is computed under a specified alternative value, not under H0.
