Type I and Type II Errors and Power: Contextual Guide

AP Statistics Topic Guide

Type I and Type II Errors and Power: Contextual Guide

Connect decisions in a significance test to their possible consequences: a Type I error rejects a true null, a Type II error fails to reject a false null, and power is the probability of detecting a specified real effect.

StatusCurrent AP Statistics inference concept

Main keywordtype i type ii errors power

Worked analysis24 cases

Focused practice20 MCQs + 8 FRQs

Study progress0 completed

Type I and Type II Errors and Power: Contextual Guide: direct answer

In a type i type ii errors power problem, begin by identifying the population target and the inferential role of the data. Connect decisions in a significance test to their possible consequences: a Type I error rejects a true null, a Type II error fails to reject a false null, and power is the probability of detecting a specified real effect.

This page uses type i type ii errors power as its single primary search focus. The lesson, numerical cases, and retained questions are restricted to that intent so the page does not function as a generic inference question bank.

Quick reference for Type I and Type II Errors and Power: Contextual Guide

Type I and Type II Errors and Power: Contextual Guide quick reference
Type I error	Reject a true H₀
Type II error	Fail to reject a false H₀
α	P(Type I error \| H₀ true)
β	P(Type II error \| specified alternative true)
Power	1−β
Power generally rises with	Larger n, larger true effect, or larger α, all else fixed

Concept mastery: type i type ii errors power

Type I error means rejecting a true null

A Type I error occurs when the procedure rejects H0 even though the null condition is true in the population. The probability of this error is controlled by alpha under the assumptions of the test.

Type II error means missing a real departure

A Type II error occurs when the procedure fails to reject H0 even though a specified alternative condition is true. Its probability is beta for that particular alternative value and study design.

Power is one minus beta

Power is the probability that the test correctly rejects H0 when a specified alternative value is true. Because power depends on the size of the real effect, there is not usually one universal power value for every possible alternative.

Alpha and beta describe different worlds

Alpha is calculated under H0; beta and power are calculated under a chosen alternative. Treating alpha+beta as automatically equal to one is incorrect because they are conditioned on different population states.

Larger samples generally increase power

When the true effect and alpha are fixed, a larger sample reduces sampling variability, making a real departure easier to distinguish from the null benchmark. This usually raises power without requiring a higher Type I error rate.

Larger true effects are easier to detect

Power rises when the true parameter is farther from the null value in the direction of Ha. Small effects are harder to distinguish from random sampling variation, especially with modest sample sizes.

Changing alpha creates a trade-off

A larger alpha makes rejection easier, increasing power but also increasing the chance of a Type I error. A smaller alpha protects more strongly against false rejection but generally reduces power when other features are fixed.

Consequences determine which error matters more

The labels Type I and Type II do not identify which error is more serious. Context determines the cost. A medical screening decision, manufacturing shutdown, and educational intervention can attach very different consequences to the two errors.

Power planning belongs before data collection

Choosing sample size with a desired power, meaningful effect size, variability assumption, and alpha is a design problem. Post hoc explanations cannot recover information that an underpowered study failed to collect.

A nonsignificant result is not proof of no effect

Failure to reject H0 can arise because H0 is close to true or because the study lacks enough information to detect the effect. Power considerations help distinguish “no convincing evidence” from an unjustified claim that the null has been established.

Worked analysis for type i type ii errors power

Error-and-power case 1: Medical Screening Program

Take H₀ to represent that the new protocol does not improve detection. A Type I error would mean adopting an ineffective protocol; under the test assumptions, its long-run probability is controlled at α=0.01. A Type II error would mean missing a real improvement when a specified meaningful alternative is actually true. These descriptions name the consequence in context rather than merely repeating “reject a true null” and “fail to reject a false null.”

Error-and-power case 2: Factory Quality-Control System

Take H₀ to represent that the defect rate has not decreased. A Type I error would mean claiming improvement when none exists; under the test assumptions, its long-run probability is controlled at α=0.05. A Type II error would mean failing to detect a real reduction when a specified meaningful alternative is actually true. These descriptions name the consequence in context rather than merely repeating “reject a true null” and “fail to reject a false null.”

Error-and-power case 3: School Tutoring Trial

Take H₀ to represent that the program has no positive mean effect. A Type I error would mean expanding a program with no true gain; under the test assumptions, its long-run probability is controlled at α=0.10. A Type II error would mean discarding a genuinely helpful program when a specified meaningful alternative is actually true. These descriptions name the consequence in context rather than merely repeating “reject a true null” and “fail to reject a false null.”

Error-and-power case 4: Water-Safety Monitor

Take H₀ to represent that the contaminant exceedance rate is at the legal baseline. A Type I error would mean triggering an unnecessary intervention; under the test assumptions, its long-run probability is controlled at α=0.01. A Type II error would mean failing to respond to a real exceedance when a specified meaningful alternative is actually true. These descriptions name the consequence in context rather than merely repeating “reject a true null” and “fail to reject a false null.”

Error-and-power case 5: Transit Reliability Project

Take H₀ to represent that the on-time proportion has not increased. A Type I error would mean crediting a change that did not work; under the test assumptions, its long-run probability is controlled at α=0.05. A Type II error would mean missing a real reliability gain when a specified meaningful alternative is actually true. These descriptions name the consequence in context rather than merely repeating “reject a true null” and “fail to reject a false null.”

If β=0.08 for that specified alternative, power is 1−β=0.92. Raising sample size generally improves the ability to distinguish that alternative from H₀. Raising α would also tend to increase power, but at the cost of more Type I errors. Which error deserves stronger protection depends on the practical consequences; the labels I and II do not establish the seriousness by themselves. In the Error-and-power case 5: Transit Reliability Project context, this checkpoint must be tied to the stated population and data structure before the numerical conclusion is accepted.

Error-and-power case 6: Fraud Detection Model

Take H₀ to represent that the new model has no higher detection rate. A Type I error would mean deploying an unimproved model; under the test assumptions, its long-run probability is controlled at α=0.10. A Type II error would mean rejecting a model that truly detects more fraud when a specified meaningful alternative is actually true. These descriptions name the consequence in context rather than merely repeating “reject a true null” and “fail to reject a false null.”

If β=0.15 for that specified alternative, power is 1−β=0.85. Raising sample size generally improves the ability to distinguish that alternative from H₀. Raising α would also tend to increase power, but at the cost of more Type I errors. Which error deserves stronger protection depends on the practical consequences; the labels I and II do not establish the seriousness by themselves. In the Error-and-power case 6: Fraud Detection Model context, this checkpoint must be tied to the stated population and data structure before the numerical conclusion is accepted.

Error-and-power case 7: Medical Screening Program

If β=0.22 for that specified alternative, power is 1−β=0.78. Raising sample size generally improves the ability to distinguish that alternative from H₀. Raising α would also tend to increase power, but at the cost of more Type I errors. Which error deserves stronger protection depends on the practical consequences; the labels I and II do not establish the seriousness by themselves. In the Error-and-power case 7: Medical Screening Program context, this checkpoint must be tied to the stated population and data structure before the numerical conclusion is accepted.

Error-and-power case 8: Factory Quality-Control System

If β=0.30 for that specified alternative, power is 1−β=0.70. Raising sample size generally improves the ability to distinguish that alternative from H₀. Raising α would also tend to increase power, but at the cost of more Type I errors. Which error deserves stronger protection depends on the practical consequences; the labels I and II do not establish the seriousness by themselves. In the Error-and-power case 8: Factory Quality-Control System context, this checkpoint must be tied to the stated population and data structure before the numerical conclusion is accepted.

Error-and-power case 9: School Tutoring Trial

If β=0.08 for that specified alternative, power is 1−β=0.92. Raising sample size generally improves the ability to distinguish that alternative from H₀. Raising α would also tend to increase power, but at the cost of more Type I errors. Which error deserves stronger protection depends on the practical consequences; the labels I and II do not establish the seriousness by themselves. In the Error-and-power case 9: School Tutoring Trial context, this checkpoint must be tied to the stated population and data structure before the numerical conclusion is accepted.

Error-and-power case 10: Water-Safety Monitor

If β=0.15 for that specified alternative, power is 1−β=0.85. Raising sample size generally improves the ability to distinguish that alternative from H₀. Raising α would also tend to increase power, but at the cost of more Type I errors. Which error deserves stronger protection depends on the practical consequences; the labels I and II do not establish the seriousness by themselves. In the Error-and-power case 10: Water-Safety Monitor context, this checkpoint must be tied to the stated population and data structure before the numerical conclusion is accepted.

Error-and-power case 11: Transit Reliability Project

If β=0.22 for that specified alternative, power is 1−β=0.78. Raising sample size generally improves the ability to distinguish that alternative from H₀. Raising α would also tend to increase power, but at the cost of more Type I errors. Which error deserves stronger protection depends on the practical consequences; the labels I and II do not establish the seriousness by themselves. In the Error-and-power case 11: Transit Reliability Project context, this checkpoint must be tied to the stated population and data structure before the numerical conclusion is accepted.

Error-and-power case 12: Fraud Detection Model

If β=0.30 for that specified alternative, power is 1−β=0.70. Raising sample size generally improves the ability to distinguish that alternative from H₀. Raising α would also tend to increase power, but at the cost of more Type I errors. Which error deserves stronger protection depends on the practical consequences; the labels I and II do not establish the seriousness by themselves. In the Error-and-power case 12: Fraud Detection Model context, this checkpoint must be tied to the stated population and data structure before the numerical conclusion is accepted.

Error-and-power case 13: Medical Screening Program

If β=0.08 for that specified alternative, power is 1−β=0.92. Raising sample size generally improves the ability to distinguish that alternative from H₀. Raising α would also tend to increase power, but at the cost of more Type I errors. Which error deserves stronger protection depends on the practical consequences; the labels I and II do not establish the seriousness by themselves. In the Error-and-power case 13: Medical Screening Program context, this checkpoint must be tied to the stated population and data structure before the numerical conclusion is accepted.

Error-and-power case 14: Factory Quality-Control System

If β=0.15 for that specified alternative, power is 1−β=0.85. Raising sample size generally improves the ability to distinguish that alternative from H₀. Raising α would also tend to increase power, but at the cost of more Type I errors. Which error deserves stronger protection depends on the practical consequences; the labels I and II do not establish the seriousness by themselves. In the Error-and-power case 14: Factory Quality-Control System context, this checkpoint must be tied to the stated population and data structure before the numerical conclusion is accepted.

Error-and-power case 15: School Tutoring Trial

If β=0.22 for that specified alternative, power is 1−β=0.78. Raising sample size generally improves the ability to distinguish that alternative from H₀. Raising α would also tend to increase power, but at the cost of more Type I errors. Which error deserves stronger protection depends on the practical consequences; the labels I and II do not establish the seriousness by themselves. In the Error-and-power case 15: School Tutoring Trial context, this checkpoint must be tied to the stated population and data structure before the numerical conclusion is accepted.

Error-and-power case 16: Water-Safety Monitor

If β=0.30 for that specified alternative, power is 1−β=0.70. Raising sample size generally improves the ability to distinguish that alternative from H₀. Raising α would also tend to increase power, but at the cost of more Type I errors. Which error deserves stronger protection depends on the practical consequences; the labels I and II do not establish the seriousness by themselves. In the Error-and-power case 16: Water-Safety Monitor context, this checkpoint must be tied to the stated population and data structure before the numerical conclusion is accepted.

Error-and-power case 17: Transit Reliability Project

If β=0.08 for that specified alternative, power is 1−β=0.92. Raising sample size generally improves the ability to distinguish that alternative from H₀. Raising α would also tend to increase power, but at the cost of more Type I errors. Which error deserves stronger protection depends on the practical consequences; the labels I and II do not establish the seriousness by themselves. In the Error-and-power case 17: Transit Reliability Project context, this checkpoint must be tied to the stated population and data structure before the numerical conclusion is accepted.

Error-and-power case 18: Fraud Detection Model

If β=0.15 for that specified alternative, power is 1−β=0.85. Raising sample size generally improves the ability to distinguish that alternative from H₀. Raising α would also tend to increase power, but at the cost of more Type I errors. Which error deserves stronger protection depends on the practical consequences; the labels I and II do not establish the seriousness by themselves. In the Error-and-power case 18: Fraud Detection Model context, this checkpoint must be tied to the stated population and data structure before the numerical conclusion is accepted.

Error-and-power case 19: Medical Screening Program

If β=0.22 for that specified alternative, power is 1−β=0.78. Raising sample size generally improves the ability to distinguish that alternative from H₀. Raising α would also tend to increase power, but at the cost of more Type I errors. Which error deserves stronger protection depends on the practical consequences; the labels I and II do not establish the seriousness by themselves. In the Error-and-power case 19: Medical Screening Program context, this checkpoint must be tied to the stated population and data structure before the numerical conclusion is accepted.

Error-and-power case 20: Factory Quality-Control System

If β=0.30 for that specified alternative, power is 1−β=0.70. Raising sample size generally improves the ability to distinguish that alternative from H₀. Raising α would also tend to increase power, but at the cost of more Type I errors. Which error deserves stronger protection depends on the practical consequences; the labels I and II do not establish the seriousness by themselves. In the Error-and-power case 20: Factory Quality-Control System context, this checkpoint must be tied to the stated population and data structure before the numerical conclusion is accepted.

Error-and-power case 21: School Tutoring Trial

If β=0.08 for that specified alternative, power is 1−β=0.92. Raising sample size generally improves the ability to distinguish that alternative from H₀. Raising α would also tend to increase power, but at the cost of more Type I errors. Which error deserves stronger protection depends on the practical consequences; the labels I and II do not establish the seriousness by themselves. In the Error-and-power case 21: School Tutoring Trial context, this checkpoint must be tied to the stated population and data structure before the numerical conclusion is accepted.

Error-and-power case 22: Water-Safety Monitor

If β=0.15 for that specified alternative, power is 1−β=0.85. Raising sample size generally improves the ability to distinguish that alternative from H₀. Raising α would also tend to increase power, but at the cost of more Type I errors. Which error deserves stronger protection depends on the practical consequences; the labels I and II do not establish the seriousness by themselves. In the Error-and-power case 22: Water-Safety Monitor context, this checkpoint must be tied to the stated population and data structure before the numerical conclusion is accepted.

Error-and-power case 23: Transit Reliability Project

If β=0.22 for that specified alternative, power is 1−β=0.78. Raising sample size generally improves the ability to distinguish that alternative from H₀. Raising α would also tend to increase power, but at the cost of more Type I errors. Which error deserves stronger protection depends on the practical consequences; the labels I and II do not establish the seriousness by themselves. In the Error-and-power case 23: Transit Reliability Project context, this checkpoint must be tied to the stated population and data structure before the numerical conclusion is accepted.

Error-and-power case 24: Fraud Detection Model

If β=0.30 for that specified alternative, power is 1−β=0.70. Raising sample size generally improves the ability to distinguish that alternative from H₀. Raising α would also tend to increase power, but at the cost of more Type I errors. Which error deserves stronger protection depends on the practical consequences; the labels I and II do not establish the seriousness by themselves. In the Error-and-power case 24: Fraud Detection Model context, this checkpoint must be tied to the stated population and data structure before the numerical conclusion is accepted.

Type I Type Ii Errors Power multiple-choice practice

Question 1. Type I Error, Type II Error, and Power

A public high school in Westview during a randomized pilot period tests H₀:p=0.4 against H_a:p>0.4 for the algebra benchmark completion criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.52.

A. Power is the probability that H₀ is true.
B. Decreasing sample size always raises power by making results more variable.
C. Type I rejects a true H₀; Type II fails to reject a false H₀; increasing n generally raises power.
D. Type I and Type II errors are both calculation mistakes.

Answer: C

For the public high school in Westview during a randomized pilot period, a Type I error is concluding that the population proportion meeting the algebra benchmark completion criterion exceeds 0.4 when it actually equals 0.4. A Type II error is failing to conclude it exceeds 0.4 when the true proportion is 0.52. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

Question 2. Type I Error, Type II Error, and Power

A farm cooperative in Pacific Northwest during a baseline measurement week tests H₀:p=0.4 against H_a:p>0.4 for the crop yield criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.48.

A. Type I and Type II errors are both calculation mistakes.
B. Decreasing sample size always raises power by making results more variable.
C. Power is the probability that H₀ is true.
D. Type I rejects a true H₀; Type II fails to reject a false H₀; increasing n generally raises power.

Answer: D

For the farm cooperative in Pacific Northwest during a baseline measurement week, a Type I error is concluding that the population proportion meeting the crop yield criterion exceeds 0.4 when it actually equals 0.4. A Type II error is failing to conclude it exceeds 0.4 when the true proportion is 0.48. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

Question 3. Type I Error, Type II Error, and Power

A recycling program in Capital Region during a service-improvement study tests H₀:p=0.5 against H_a:p>0.5 for the weekly material weight criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.62.

A. Power is the probability that H₀ is true.
B. Decreasing sample size always raises power by making results more variable.
C. Type I rejects a true H₀; Type II fails to reject a false H₀; increasing n generally raises power.
D. Type I and Type II errors are both calculation mistakes.

Answer: C

For the recycling program in Capital Region during a service-improvement study, a Type I error is concluding that the population proportion meeting the weekly material weight criterion exceeds 0.5 when it actually equals 0.5. A Type II error is failing to conclude it exceeds 0.5 when the true proportion is 0.62. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

Question 4. Type I Error, Type II Error, and Power

A solar installer in Atlantic Corridor during a service-improvement study tests H₀:p=0.4 against H_a:p>0.4 for the daily energy output criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.48.

A. Type I and Type II errors are both calculation mistakes.
B. Power is the probability that H₀ is true.
C. Type I rejects a true H₀; Type II fails to reject a false H₀; increasing n generally raises power.
D. Decreasing sample size always raises power by making results more variable.

Answer: C

For the solar installer in Atlantic Corridor during a service-improvement study, a Type I error is concluding that the population proportion meeting the daily energy output criterion exceeds 0.4 when it actually equals 0.4. A Type II error is failing to conclude it exceeds 0.4 when the true proportion is 0.48. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

Question 5. Type I Error, Type II Error, and Power

A regional manufacturer in Great Lakes during a fall 2026 audit tests H₀:p=0.4 against H_a:p>0.4 for the part diameter criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.52.

A. Type I rejects a true H₀; Type II fails to reject a false H₀; increasing n generally raises power.
B. Power is the probability that H₀ is true.
C. Decreasing sample size always raises power by making results more variable.
D. Type I and Type II errors are both calculation mistakes.

Answer: A

For the regional manufacturer in Great Lakes during a fall 2026 audit, a Type I error is concluding that the population proportion meeting the part diameter criterion exceeds 0.4 when it actually equals 0.4. A Type II error is failing to conclude it exceeds 0.4 when the true proportion is 0.52. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

Question 6. Type I Error, Type II Error, and Power

A grocery cooperative in Mountain Region during a pre-exam training cycle tests H₀:p=0.5 against H_a:p>0.5 for the checkout time criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.58.

A. Type I and Type II errors are both calculation mistakes.
B. Decreasing sample size always raises power by making results more variable.
C. Type I rejects a true H₀; Type II fails to reject a false H₀; increasing n generally raises power.
D. Power is the probability that H₀ is true.

Answer: C

For the grocery cooperative in Mountain Region during a pre-exam training cycle, a Type I error is concluding that the population proportion meeting the checkout time criterion exceeds 0.5 when it actually equals 0.5. A Type II error is failing to conclude it exceeds 0.5 when the true proportion is 0.58. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

Question 7. Type I Error, Type II Error, and Power

A regional hospital in Central County during a fall 2026 audit tests H₀:p=0.6 against H_a:p>0.6 for the appointment completion criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.68.

A. Decreasing sample size always raises power by making results more variable.
B. Type I and Type II errors are both calculation mistakes.
C. Type I rejects a true H₀; Type II fails to reject a false H₀; increasing n generally raises power.
D. Power is the probability that H₀ is true.

Answer: C

For the regional hospital in Central County during a fall 2026 audit, a Type I error is concluding that the population proportion meeting the appointment completion criterion exceeds 0.6 when it actually equals 0.6. A Type II error is failing to conclude it exceeds 0.6 when the true proportion is 0.68. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

Question 8. Type I Error, Type II Error, and Power

A community college in Great Lakes during a winter readiness review tests H₀:p=0.5 against H_a:p>0.5 for the course completion criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.62.

A. Power is the probability that H₀ is true.
B. Type I and Type II errors are both calculation mistakes.
C. Decreasing sample size always raises power by making results more variable.
D. Type I rejects a true H₀; Type II fails to reject a false H₀; increasing n generally raises power.

Answer: D

For the community college in Great Lakes during a winter readiness review, a Type I error is concluding that the population proportion meeting the course completion criterion exceeds 0.5 when it actually equals 0.5. A Type II error is failing to conclude it exceeds 0.5 when the true proportion is 0.62. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

Question 9. Type I Error, Type II Error, and Power

A state park in Prairie District during a randomized pilot period tests H₀:p=0.6 against H_a:p>0.6 for the trail-use duration criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.68.

A. Decreasing sample size always raises power by making results more variable.
B. Power is the probability that H₀ is true.
C. Type I rejects a true H₀; Type II fails to reject a false H₀; increasing n generally raises power.
D. Type I and Type II errors are both calculation mistakes.

Answer: C

For the state park in Prairie District during a randomized pilot period, a Type I error is concluding that the population proportion meeting the trail-use duration criterion exceeds 0.6 when it actually equals 0.6. A Type II error is failing to conclude it exceeds 0.6 when the true proportion is 0.68. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

Question 10. Type I Error, Type II Error, and Power

A digital learning platform in Central County during a quarterly performance study tests H₀:p=0.5 against H_a:p>0.5 for the lesson completion criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.58.

A. Type I rejects a true H₀; Type II fails to reject a false H₀; increasing n generally raises power.
B. Type I and Type II errors are both calculation mistakes.
C. Power is the probability that H₀ is true.
D. Decreasing sample size always raises power by making results more variable.

Answer: A

For the digital learning platform in Central County during a quarterly performance study, a Type I error is concluding that the population proportion meeting the lesson completion criterion exceeds 0.5 when it actually equals 0.5. A Type II error is failing to conclude it exceeds 0.5 when the true proportion is 0.58. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

Question 11. Type I Error, Type II Error, and Power

A regional airport authority in Midwest consortium during a yearly program evaluation tests H₀:p=0.6 against H_a:p>0.6 for the security wait time criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.72.

A. Type I rejects a true H₀; Type II fails to reject a false H₀; increasing n generally raises power.
B. Power is the probability that H₀ is true.
C. Decreasing sample size always raises power by making results more variable.
D. Type I and Type II errors are both calculation mistakes.

Answer: A

For the regional airport authority in Midwest consortium during a yearly program evaluation, a Type I error is concluding that the population proportion meeting the security wait time criterion exceeds 0.6 when it actually equals 0.6. A Type II error is failing to conclude it exceeds 0.6 when the true proportion is 0.72. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

Question 12. Type I Error, Type II Error, and Power

A solar installer in Atlantic Corridor during a pre-exam training cycle tests H₀:p=0.6 against H_a:p>0.6 for the daily energy output criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.68.

A. Decreasing sample size always raises power by making results more variable.
B. Type I and Type II errors are both calculation mistakes.
C. Power is the probability that H₀ is true.
D. Type I rejects a true H₀; Type II fails to reject a false H₀; increasing n generally raises power.

Answer: D

For the solar installer in Atlantic Corridor during a pre-exam training cycle, a Type I error is concluding that the population proportion meeting the daily energy output criterion exceeds 0.6 when it actually equals 0.6. A Type II error is failing to conclude it exceeds 0.6 when the true proportion is 0.68. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

Question 13. Type I Error, Type II Error, and Power

A recycling program in Pacific Northwest during a spring 2027 pilot tests H₀:p=0.4 against H_a:p>0.4 for the weekly material weight criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.52.

A. Power is the probability that H₀ is true.
B. Type I rejects a true H₀; Type II fails to reject a false H₀; increasing n generally raises power.
C. Decreasing sample size always raises power by making results more variable.
D. Type I and Type II errors are both calculation mistakes.

Answer: B

For the recycling program in Pacific Northwest during a spring 2027 pilot, a Type I error is concluding that the population proportion meeting the weekly material weight criterion exceeds 0.4 when it actually equals 0.4. A Type II error is failing to conclude it exceeds 0.4 when the true proportion is 0.52. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

Question 14. Type I Error, Type II Error, and Power

A state park in Westview during a baseline measurement week tests H₀:p=0.4 against H_a:p>0.4 for the trail-use duration criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.52.

A. Type I and Type II errors are both calculation mistakes.
B. Decreasing sample size always raises power by making results more variable.
C. Type I rejects a true H₀; Type II fails to reject a false H₀; increasing n generally raises power.
D. Power is the probability that H₀ is true.

Answer: C

For the state park in Westview during a baseline measurement week, a Type I error is concluding that the population proportion meeting the trail-use duration criterion exceeds 0.4 when it actually equals 0.4. A Type II error is failing to conclude it exceeds 0.4 when the true proportion is 0.52. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

Question 15. Type I Error, Type II Error, and Power

A county library in New England network during a school-year data collection tests H₀:p=0.5 against H_a:p>0.5 for the weekly program attendance criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.62.

A. Type I rejects a true H₀; Type II fails to reject a false H₀; increasing n generally raises power.
B. Power is the probability that H₀ is true.
C. Type I and Type II errors are both calculation mistakes.
D. Decreasing sample size always raises power by making results more variable.

Answer: A

For the county library in New England network during a school-year data collection, a Type I error is concluding that the population proportion meeting the weekly program attendance criterion exceeds 0.5 when it actually equals 0.5. A Type II error is failing to conclude it exceeds 0.5 when the true proportion is 0.62. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

Question 16. Type I Error, Type II Error, and Power

A digital learning platform in Capital Region during a fall 2026 audit tests H₀:p=0.6 against H_a:p>0.6 for the lesson completion criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.68.

A. Power is the probability that H₀ is true.
B. Type I rejects a true H₀; Type II fails to reject a false H₀; increasing n generally raises power.
C. Type I and Type II errors are both calculation mistakes.
D. Decreasing sample size always raises power by making results more variable.

Answer: B

For the digital learning platform in Capital Region during a fall 2026 audit, a Type I error is concluding that the population proportion meeting the lesson completion criterion exceeds 0.6 when it actually equals 0.6. A Type II error is failing to conclude it exceeds 0.6 when the true proportion is 0.68. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

Question 17. Type I Error, Type II Error, and Power

A farm cooperative in Metro East during a follow-up evaluation period tests H₀:p=0.5 against H_a:p>0.5 for the crop yield criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.58.

A. Type I and Type II errors are both calculation mistakes.
B. Decreasing sample size always raises power by making results more variable.
C. Type I rejects a true H₀; Type II fails to reject a false H₀; increasing n generally raises power.
D. Power is the probability that H₀ is true.

Answer: C

For the farm cooperative in Metro East during a follow-up evaluation period, a Type I error is concluding that the population proportion meeting the crop yield criterion exceeds 0.5 when it actually equals 0.5. A Type II error is failing to conclude it exceeds 0.5 when the true proportion is 0.58. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

Question 18. Type I Error, Type II Error, and Power

A municipal water office in Metro East during a summer implementation review tests H₀:p=0.4 against H_a:p>0.4 for the monthly household use criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.52.

A. Type I rejects a true H₀; Type II fails to reject a false H₀; increasing n generally raises power.
B. Power is the probability that H₀ is true.
C. Type I and Type II errors are both calculation mistakes.
D. Decreasing sample size always raises power by making results more variable.

Answer: A

For the municipal water office in Metro East during a summer implementation review, a Type I error is concluding that the population proportion meeting the monthly household use criterion exceeds 0.4 when it actually equals 0.4. A Type II error is failing to conclude it exceeds 0.4 when the true proportion is 0.52. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

Question 19. Type I Error, Type II Error, and Power

A county election office in Metro East during a semester-long cohort study tests H₀:p=0.5 against H_a:p>0.5 for the ballot-processing time criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.58.

A. Decreasing sample size always raises power by making results more variable.
B. Type I and Type II errors are both calculation mistakes.
C. Power is the probability that H₀ is true.
D. Type I rejects a true H₀; Type II fails to reject a false H₀; increasing n generally raises power.

Answer: D

For the county election office in Metro East during a semester-long cohort study, a Type I error is concluding that the population proportion meeting the ballot-processing time criterion exceeds 0.5 when it actually equals 0.5. A Type II error is failing to conclude it exceeds 0.5 when the true proportion is 0.58. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

Question 20. Type I Error, Type II Error, and Power

A county election office in Cedar Grove during a winter readiness review tests H₀:p=0.5 against H_a:p>0.5 for the ballot-processing time criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.58.

A. Type I and Type II errors are both calculation mistakes.
B. Decreasing sample size always raises power by making results more variable.
C. Power is the probability that H₀ is true.
D. Type I rejects a true H₀; Type II fails to reject a false H₀; increasing n generally raises power.

Answer: D

For the county election office in Cedar Grove during a winter readiness review, a Type I error is concluding that the population proportion meeting the ballot-processing time criterion exceeds 0.5 when it actually equals 0.5. A Type II error is failing to conclude it exceeds 0.5 when the true proportion is 0.58. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

Type I Type Ii Errors Power free-response practice

FRQ set 1: Type I Error, Type II Error, and Power

Scenario. A regional manufacturer in Pacific Northwest during a follow-up evaluation period tests H₀:p=0.4 against H_a:p>0.4 for the part diameter criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.48.

State the population parameter and hypotheses, including direction and group order.
Verify the procedure conditions using evidence from the prompt.
Compute the test statistic and p-value from the correct null model or expected counts.
Make a decision at the stated significance level and conclude about the population without treating the p-value as the probability the null is true.

Model response

For the regional manufacturer in Pacific Northwest during a follow-up evaluation period, a Type I error is concluding that the population proportion meeting the part diameter criterion exceeds 0.4 when it actually equals 0.4. A Type II error is failing to conclude it exceeds 0.4 when the true proportion is 0.48. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

FRQ set 2: Type I Error, Type II Error, and Power

Scenario. A housing authority in Central County during a spring 2027 pilot tests H₀:p=0.5 against H_a:p>0.5 for the application processing time criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.62.

State the population parameter and hypotheses, including direction and group order.
Verify the procedure conditions using evidence from the prompt.
Compute the test statistic and p-value from the correct null model or expected counts.
Make a decision at the stated significance level and conclude about the population without treating the p-value as the probability the null is true.

Model response

For the housing authority in Central County during a spring 2027 pilot, a Type I error is concluding that the population proportion meeting the application processing time criterion exceeds 0.5 when it actually equals 0.5. A Type II error is failing to conclude it exceeds 0.5 when the true proportion is 0.62. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

FRQ set 3: Type I Error, Type II Error, and Power

Scenario. A public health department in New England network during a winter readiness review tests H₀:p=0.4 against H_a:p>0.4 for the vaccination appointment completion criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.48.

State the population parameter and hypotheses, including direction and group order.
Verify the procedure conditions using evidence from the prompt.
Compute the test statistic and p-value from the correct null model or expected counts.
Make a decision at the stated significance level and conclude about the population without treating the p-value as the probability the null is true.

Model response

For the public health department in New England network during a winter readiness review, a Type I error is concluding that the population proportion meeting the vaccination appointment completion criterion exceeds 0.4 when it actually equals 0.4. A Type II error is failing to conclude it exceeds 0.4 when the true proportion is 0.48. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

FRQ set 4: Type I Error, Type II Error, and Power

Scenario. A municipal emergency dispatch center in Desert County during a regional benchmarking study tests H₀:p=0.6 against H_a:p>0.6 for the response time criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.68.

State the population parameter and hypotheses, including direction and group order.
Verify the procedure conditions using evidence from the prompt.
Compute the test statistic and p-value from the correct null model or expected counts.
Make a decision at the stated significance level and conclude about the population without treating the p-value as the probability the null is true.

Model response

For the municipal emergency dispatch center in Desert County during a regional benchmarking study, a Type I error is concluding that the population proportion meeting the response time criterion exceeds 0.6 when it actually equals 0.6. A Type II error is failing to conclude it exceeds 0.6 when the true proportion is 0.68. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

FRQ set 5: Type I Error, Type II Error, and Power

Scenario. A public health department in New England network during a six-week field trial tests H₀:p=0.6 against H_a:p>0.6 for the vaccination appointment completion criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.72.

State the population parameter and hypotheses, including direction and group order.
Verify the procedure conditions using evidence from the prompt.
Compute the test statistic and p-value from the correct null model or expected counts.
Make a decision at the stated significance level and conclude about the population without treating the p-value as the probability the null is true.

Model response

For the public health department in New England network during a six-week field trial, a Type I error is concluding that the population proportion meeting the vaccination appointment completion criterion exceeds 0.6 when it actually equals 0.6. A Type II error is failing to conclude it exceeds 0.6 when the true proportion is 0.72. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

FRQ set 6: Type I Error, Type II Error, and Power

Scenario. A public health department in Midwest consortium during a community outreach cycle tests H₀:p=0.5 against H_a:p>0.5 for the vaccination appointment completion criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.62.

State the population parameter and hypotheses, including direction and group order.
Verify the procedure conditions using evidence from the prompt.
Compute the test statistic and p-value from the correct null model or expected counts.
Make a decision at the stated significance level and conclude about the population without treating the p-value as the probability the null is true.

Model response

For the public health department in Midwest consortium during a community outreach cycle, a Type I error is concluding that the population proportion meeting the vaccination appointment completion criterion exceeds 0.5 when it actually equals 0.5. A Type II error is failing to conclude it exceeds 0.5 when the true proportion is 0.62. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

FRQ set 7: Type I Error, Type II Error, and Power

Scenario. A digital learning platform in Capital Region during a follow-up evaluation period tests H₀:p=0.5 against H_a:p>0.5 for the lesson completion criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.62.

State the population parameter and hypotheses, including direction and group order.
Verify the procedure conditions using evidence from the prompt.
Compute the test statistic and p-value from the correct null model or expected counts.
Make a decision at the stated significance level and conclude about the population without treating the p-value as the probability the null is true.

Model response

For the digital learning platform in Capital Region during a follow-up evaluation period, a Type I error is concluding that the population proportion meeting the lesson completion criterion exceeds 0.5 when it actually equals 0.5. A Type II error is failing to conclude it exceeds 0.5 when the true proportion is 0.62. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

FRQ set 8: Type I Error, Type II Error, and Power

Scenario. A municipal water office in Westview during a regional benchmarking study tests H₀:p=0.5 against H_a:p>0.5 for the monthly household use criterion. Describe Type I and Type II errors, then state one change that generally increases power against p=0.62.

State the population parameter and hypotheses, including direction and group order.
Verify the procedure conditions using evidence from the prompt.
Compute the test statistic and p-value from the correct null model or expected counts.
Make a decision at the stated significance level and conclude about the population without treating the p-value as the probability the null is true.

Model response

For the municipal water office in Westview during a regional benchmarking study, a Type I error is concluding that the population proportion meeting the monthly household use criterion exceeds 0.5 when it actually equals 0.5. A Type II error is failing to conclude it exceeds 0.5 when the true proportion is 0.62. Increasing sample size or α generally increases power against that alternative; improving measurement can also help.

Next steps after mastering type i type ii errors power

Continue by taking a real decision context and writing the concrete consequence of each error before attaching the labels Type I or Type II. Then decide which consequence is more costly and explain whether that would justify a smaller alpha, a larger sample, or both. This turns error terminology into a study-design decision.

For power review, hold alpha and the meaningful effect size fixed while increasing n, then hold n fixed while moving the true parameter farther from H₀. Explain why both changes generally increase power through different mechanisms. Finally, state why a nonsignificant result from a low-power study cannot be treated as strong evidence that the null is true.