AP Statistics Quiz: Potential Errors When Performing Tests
20 questions · exam conditions
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Potential Errors When Performing TestsQuestion 1 of 20

A manufacturer tests whether the mean lifetime of a battery is greater than 8 hours. They test H0:μ=8H_0: \mu=8 vs. Ha:μ>8H_a: \mu>8 at α=0.05\alpha=0.05. The test result is to reject H0H_0 and claim the mean lifetime exceeds 8 hours. In reality, the true mean lifetime is μ=8.6\mu=8.6 hours. Which type of error was made?

Type I error: concluding μ>8\mu>8 when in fact μ=8\mu=8
Type II error: failing to reject H0H_0 when μ>8\mu>8
Type II error: rejecting H0H_0 when μ=8\mu=8
No error: the conclusion matches the true state of the population
Type I error: failing to reject H0H_0 when μ>8\mu>8
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AP Statistics Quiz

AP Statistics Quiz: Potential Errors When Performing Tests

Practice Potential Errors When Performing Tests in AP Statistics with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Potential Errors When Performing Tests, giving you a quick way to practice the rules, question types, and explanations that matter most for AP Statistics.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A manufacturer tests whether the mean lifetime of a battery is greater than 8 hours. They test H0:μ=8H_0: \mu=8 vs. Ha:μ>8H_a: \mu>8 at α=0.05\alpha=0.05. The test result is to reject H0H_0 and claim the mean lifetime exceeds 8 hours. In reality, the true mean lifetime is μ=8.6\mu=8.6 hours. Which type of error was made?

  1. Type I error: concluding μ>8\mu>8 when in fact μ=8\mu=8
  2. Type II error: failing to reject H0H_0 when μ>8\mu>8
  3. Type II error: rejecting H0H_0 when μ=8\mu=8
  4. No error: the conclusion matches the true state of the population (correct answer)
  5. Type I error: failing to reject H0H_0 when μ>8\mu>8

Explanation: This question tests understanding of correct decisions in hypothesis testing. The manufacturer rejected H₀ (concluded μ > 8) when the alternative hypothesis is actually true (μ = 8.6 > 8). No error was made because the decision matches reality: the test correctly detected that the mean lifetime exceeds 8 hours. When we reject H₀ and H₀ is false (Ha is true), we've made a correct decision. Type I errors occur when we reject a true H₀, and Type II errors occur when we fail to reject a false H₀ - neither applies here.

Question 2

A hospital tests whether the mean waiting time in the emergency room is less than 30 minutes after adding staff. They test H0:μ=30H_0: \mu=30 vs. Ha:μ<30H_a: \mu<30 at α=0.05\alpha=0.05. They fail to reject H0H_0 and state there is not convincing evidence the mean waiting time is below 30 minutes. In reality, the true mean waiting time is μ=30\mu=30 minutes. Which type of error was made?

  1. Type II error: failing to detect that the mean is below 30 when it is
  2. Type I error: concluding the mean is below 30 when it is not
  3. No error: the decision is consistent with the true population mean (correct answer)
  4. Type I error: failing to reject H0H_0 when μ<30\mu<30
  5. Type II error: concluding the mean is below 30 when it is not

Explanation: This question tests understanding of correct decisions in hypothesis testing. The hospital failed to reject H₀ (concluded no evidence μ < 30) when the null hypothesis is actually true (μ = 30). No error was made because the decision matches reality: the test correctly concluded there's no evidence the mean is below 30 minutes, and indeed it equals 30. When we fail to reject H₀ and H₀ is true, we've made a correct decision. Type I errors occur when we reject a true H₀, and Type II errors occur when we fail to reject a false H₀ - neither applies here.

Question 3

A hospital tests whether a new sterilization procedure reduces the mean number of bacteria colonies on instruments below 12 colonies. They use H0:μ=12H_0: \mu=12 versus Ha:μ<12H_a: \mu<12 at α=0.01\alpha=0.01. The test is not statistically significant, so they do not switch procedures. In reality, the true population mean under the new procedure is μ=9\mu=9 colonies. Which type of error was made?

  1. Type II error (failing to reject a false null hypothesis) (correct answer)
  2. No error was made because α=0.01\alpha=0.01 is very strict
  3. Type I error (rejecting a true null hypothesis)
  4. Type II error (rejecting a true null hypothesis)
  5. Type I error (failing to reject a false null hypothesis)

Explanation: This question demonstrates a Type II error in hypothesis testing. The hospital failed to reject the null hypothesis (μ = 12 colonies) when in reality the alternative hypothesis was true (μ = 9 colonies < 12 colonies). This is a Type II error - failing to reject a false null hypothesis. The new procedure actually was better (fewer bacteria colonies), but the test failed to detect this improvement. The very strict significance level (α = 0.01) makes Type II errors more likely because we require overwhelming evidence to reject H₀. This example shows how being too conservative (small α) can lead to missing real improvements, which is particularly concerning in medical contexts where better procedures could improve patient safety.

Question 4

A streaming company tests whether a new recommendation algorithm increases the mean number of minutes watched per user above the current mean of 50 minutes. They test H0:μ=50H_0: \mu=50 versus Ha:μ>50H_a: \mu>50 at α=0.05\alpha=0.05. The result is statistically significant, so they conclude the algorithm increases watch time. In reality, the true population mean with the new algorithm is μ=50\mu=50 minutes (no change). Which type of error was made?

  1. Type II error (failing to reject a false null hypothesis)
  2. Type I error (rejecting a true null hypothesis) (correct answer)
  3. Type I error (failing to reject a false null hypothesis)
  4. No error was made because the company used α=0.05\alpha=0.05
  5. Type II error (rejecting a true null hypothesis)

Explanation: This question illustrates a Type I error in hypothesis testing. The streaming company rejected the null hypothesis (concluded the algorithm increases watch time) when the null hypothesis was actually true (μ = 50 minutes, no change). This is a Type I error - rejecting a true null hypothesis. The statistically significant result was a false positive, leading to an incorrect business decision. Type I errors occur with probability α = 0.05, meaning this outcome will happen about 5% of the time even when following proper procedures. Understanding that statistical significance doesn't guarantee practical truth helps students appreciate why we control but cannot eliminate Type I error risk.

Question 5

A school district tests whether a new tutoring program changes the mean math score compared with the current mean of 75. They perform a two-sided test with H0:μ=75H_0: \mu=75 versus Ha:μ≠75H_a: \mu\neq 75 at α=0.10\alpha=0.10. The test is not statistically significant, so they do not adopt the program, concluding there is not enough evidence of a change in mean score. In reality, the true population mean score with the tutoring program is μ=75\mu=75 exactly. Which type of error was made?

  1. Type I error (rejecting a true null hypothesis)
  2. Type II error (failing to reject a false null hypothesis)
  3. No error was made (correct answer)
  4. Type I error (failing to reject a false null hypothesis)
  5. Type II error (rejecting a true null hypothesis)

Explanation: This question demonstrates a correct decision in hypothesis testing. The school district failed to reject the null hypothesis (μ = 75), and in reality, the null hypothesis was true (μ = 75). This represents a correct decision - no error was made. When we fail to reject a true null hypothesis, we've made the right choice. This scenario helps students understand that not all hypothesis test outcomes involve errors. The two-sided alternative (μ ≠ 75) and higher significance level (α = 0.10) don't change the fact that the correct decision was made. Recognizing correct decisions is as important as identifying errors in understanding the complete framework of hypothesis testing outcomes.

Question 6

A quality-control engineer tests whether the proportion of defective parts produced by a machine is greater than 0.02. They test H0:p=0.02H_0: p=0.02 versus Ha:p>0.02H_a: p>0.02 at α=0.05\alpha=0.05. The test is statistically significant, so they conclude the defect rate is greater than 0.02 and shut the machine down for maintenance. In reality, the true population defect proportion is p=0.02p=0.02. Which type of error was made?

  1. Type II error (failing to reject a false null hypothesis)
  2. Type II error (rejecting a true null hypothesis)
  3. No error was made because maintenance is a safe choice
  4. Type I error (rejecting a true null hypothesis) (correct answer)
  5. Type I error (failing to reject a false null hypothesis)

Explanation: This question illustrates a Type I error in quality control. The engineer rejected the null hypothesis (concluded p > 0.02) when the null hypothesis was actually true (p = 0.02). This is a Type I error - rejecting a true null hypothesis. The statistically significant result led to unnecessary machine maintenance when the defect rate was actually at the acceptable level. In quality control, Type I errors can lead to unnecessary downtime and costs. The irony is that while trying to maintain quality, the false alarm disrupted production unnecessarily. This example helps students understand that Type I errors have real-world consequences and why controlling the significance level α is important in balancing error risks.

Question 7

A city tests whether the proportion of commuters who use public transit is greater than 0.25 after a fare reduction. They test H0:p=0.25H_0: p=0.25 vs. Ha:p>0.25H_a: p>0.25 at α=0.05\alpha=0.05. The city fails to reject H0H_0 and states there is not convincing evidence the fare reduction increased transit use. In reality, the true proportion is p=0.30p=0.30. Which type of error was made?

  1. Type I error: concluding transit use increased when it did not
  2. Type II error: failing to detect an increase that is real (correct answer)
  3. No error: failing to reject H0H_0 means p=0.25p=0.25
  4. Type I error: failing to reject H0H_0 when p>0.25p>0.25
  5. Type II error: concluding transit use increased when it did not

Explanation: This question tests understanding of Type II errors in one-sided tests. The city failed to reject H₀ (concluded no evidence of increased transit use) when the alternative hypothesis is actually true (p = 0.30 > 0.25, transit use DID increase). A Type II error occurs when we fail to reject a false null hypothesis - we miss detecting a real effect. This matches the scenario: the fare reduction actually increased transit use to 30%, but the test failed to detect this increase. Type I errors involve rejecting a true H₀, which cannot occur when we fail to reject.

Question 8

A pharmaceutical company tests whether a generic drug is less effective than the brand-name drug by comparing mean symptom-reduction scores. They set up H0:μG−μB=0H_0: \mu_G-\mu_B=0 vs. Ha:μG−μB<0H_a: \mu_G-\mu_B<0 at α=0.05\alpha=0.05. The analysis leads them to reject H0H_0 and claim the generic is less effective. In reality, the generic and brand are equally effective (the true difference is μG−μB=0\mu_G-\mu_B=0). Which type of error was made?

  1. Type II error: failing to detect that the generic is less effective
  2. Type I error: concluding the generic is less effective when it is not (correct answer)
  3. No error: rejecting H0H_0 guarantees the generic is less effective
  4. Type II error: concluding the generic is less effective when it is not
  5. Type I error: failing to reject H0H_0 when the generic is less effective

Explanation: This question tests understanding of Type I errors with difference tests. The company rejected H₀ (concluded the generic is less effective) when the null hypothesis is actually true (μG - μB = 0, drugs are equally effective). A Type I error occurs when we reject a true null hypothesis - we falsely detect a difference that doesn't exist. This is exactly the situation: the drugs are equally effective, but the test incorrectly concluded the generic is inferior. Type II errors involve failing to reject a false H₀, which doesn't apply when H₀ is rejected.

Question 9

A tech company tests whether a new interface reduces average customer support time. They use H0:μ=12H_0: \mu=12 minutes vs. Ha:μ<12H_a: \mu<12 minutes at α=0.05\alpha=0.05. They reject H0H_0 and announce the interface reduced mean support time. In reality, the true mean support time with the new interface is still μ=12\mu=12 minutes. Which type of error was made?

  1. Type II error: failing to detect a real reduction in support time
  2. Type I error: concluding there is a reduction when there is none (correct answer)
  3. Type II error: concluding there is a reduction when there is none
  4. No error: rejecting H0H_0 proves the mean is less than 12
  5. Type I error: failing to reject H0H_0 when the mean is less than 12

Explanation: This question tests understanding of Type I errors in one-sided tests. The company rejected H₀ (concluded support time was reduced) when the null hypothesis is actually true (μ = 12, no reduction). A Type I error occurs when we reject a true null hypothesis - we falsely claim an improvement that doesn't exist. This is precisely what happened: the new interface doesn't actually reduce support time, but the test incorrectly concluded it does. Type II errors involve failing to reject a false H₀, which doesn't apply when H₀ is rejected.

Question 10

A quality-control engineer tests whether the mean fill amount of a cereal box is less than the labeled 500 g. The hypotheses are H0:μ=500H_0: \mu=500 vs. Ha:μ<500H_a: \mu<500 at α=0.01\alpha=0.01. The test result is to fail to reject H0H_0, so the engineer reports there is not convincing evidence of underfilling. In reality, the true mean fill is μ=495\mu=495 g (the boxes are underfilled). Which type of error was made?

  1. Type I error: concluding the boxes are underfilled when they are not
  2. No error was made because failing to reject H0H_0 proves μ=500\mu=500
  3. Type II error: failing to detect underfilling when it is real (correct answer)
  4. Type I error: failing to reject H0H_0 when μ<500\mu<500
  5. Type II error: concluding the boxes are underfilled when they are not

Explanation: This question tests understanding of Type II errors in hypothesis testing. The engineer failed to reject H₀ (concluded no evidence of underfilling) when the alternative hypothesis is actually true (μ = 495 < 500, boxes ARE underfilled). A Type II error occurs when we fail to reject a false null hypothesis - we miss detecting a real effect. This matches the scenario perfectly: the boxes are actually underfilled but the test failed to detect this problem. Type I errors involve rejecting a true null hypothesis, which cannot happen when we fail to reject H₀.

Question 11

A public health team tests whether a new text-message reminder increases the proportion of patients who get a flu shot. They test H0:p=0.40H_0: p=0.40 vs. Ha:p>0.40H_a: p>0.40 at significance level α=0.05\alpha=0.05. After analyzing the sample, they reject H0H_0 and announce the reminders increase the flu-shot rate. In reality, the true population proportion with reminders is still p=0.40p=0.40 (no increase). Which type of error was made?

  1. Type II error: concluding there is an increase when there is none
  2. Type I error: concluding there is an increase when there is none (correct answer)
  3. Type I error: failing to detect an increase that is real
  4. Type II error: failing to reject H0H_0 when p>0.40p>0.40
  5. No error was made because rejecting H0H_0 is always correct when α=0.05\alpha=0.05

Explanation: This question tests understanding of Type I errors in hypothesis testing. The scenario describes rejecting H₀ (concluding there IS an increase) when the null hypothesis is actually true (p = 0.40, no increase). A Type I error occurs when we reject a true null hypothesis - we falsely detect an effect that doesn't exist. This is exactly what happened here: the health team concluded the reminders increase flu-shot rates when in reality they don't. Type II errors involve failing to reject a false null hypothesis, which is not the case here since H₀ was rejected.

Question 12

A school district tests whether a new tutoring program changes the mean math score. They use H0:μ=70H_0: \mu=70 vs. Ha:μ≠70H_a: \mu\neq 70 with α=0.10\alpha=0.10. The district rejects H0H_0 and concludes the program changes the mean score. In truth, the program has no effect and the population mean remains μ=70\mu=70. Which type of error was made?

  1. Type II error: concluding the mean changed when it did not
  2. No error: rejecting H0H_0 means the mean must be different
  3. Type I error: concluding the mean changed when it did not (correct answer)
  4. Type II error: failing to detect a real change in the mean
  5. Type I error: failing to reject H0H_0 when the mean is different

Explanation: This question tests understanding of Type I errors with two-sided tests. The district rejected H₀ (concluded the mean changed) when the null hypothesis is actually true (μ = 70, no change). A Type I error occurs when we reject a true null hypothesis - we falsely conclude there's a difference when none exists. This is precisely what happened: the tutoring program has no effect, but the test incorrectly concluded it changes scores. Type II errors involve failing to reject H₀ when it's false, which doesn't apply here since H₀ was rejected.

Question 13

A meteorologist tests whether the mean daily high temperature in a city this month is less than the long-term mean of 80°F. They test H0:μ=80H_0: \mu=80 versus Ha:μ<80H_a: \mu<80 at α=0.05\alpha=0.05. The result is not statistically significant, so they conclude there is not enough evidence that the mean is below 80°F. In reality, the true population mean for the month is μ=80\mu=80°F. Which type of error was made?

  1. Type I error (rejecting a true null hypothesis)
  2. Type II error (failing to reject a false null hypothesis)
  3. Type II error (rejecting a true null hypothesis)
  4. No error was made (correct answer)
  5. Type I error (failing to reject a false null hypothesis)

Explanation: This question illustrates a correct decision in hypothesis testing. The meteorologist failed to reject the null hypothesis (μ = 80°F), and the null hypothesis was actually true (μ = 80°F). No error was made - this is a correct decision. When we fail to reject a true null hypothesis, we've properly concluded there's insufficient evidence for the alternative when indeed no effect exists. This scenario reinforces that hypothesis testing can lead to correct conclusions, not just errors. Understanding all four possible outcomes (two correct decisions and two types of errors) helps students see hypothesis testing as a decision-making framework where we aim to minimize errors while recognizing that correct decisions are the desired outcome.

Question 14

A hospital tests whether a new triage protocol changes the proportion of patients seen within 15 minutes from the current rate of 0.80. The hypotheses are H0:p=0.80H_0: p = 0.80 and Ha:p≠0.80H_a: p \ne 0.80. The hospital rejects H0H_0 at α=0.05\alpha = 0.05. In fact, the true proportion under the new protocol is still p=0.80p = 0.80. Which type of error was made?

  1. Type II error (failing to reject a false null hypothesis)
  2. Type I error (rejecting a true null hypothesis) (correct answer)
  3. No error was made because rejecting H0H_0 means the protocol works
  4. Type I error (failing to reject a false null hypothesis)
  5. Type II error (rejecting a true null hypothesis)

Explanation: This question tests the skill of spotting Type I errors in two-sided hypothesis tests. The decision was to reject H0 (p = 0.80), but in reality p = 0.80, so H0 is true, resulting in a Type I error. Choice B correctly describes it as Type I (rejecting true H0). A common distractor is choice A, which is Type II but inapplicable since H0 was rejected. Another distractor is choice C, claiming no error because rejecting means the protocol works, ignoring that H0 is true. For a mini-lesson, in two-sided tests, Type I error happens when we reject a true null, concluding a difference when none exists; Type II is failing to detect a real difference; the alternative ≠ allows detection in either direction.

Question 15

A public health department tests whether the proportion of residents who support a proposed policy is greater than 0.50. They test H0:p=0.50H_0: p=0.50 vs. Ha:p>0.50H_a: p>0.50 at α=0.05\alpha=0.05. The p-value is 0.11, so they fail to reject H0H_0 and conclude there is not convincing evidence that more than half support the policy. In reality, the true proportion is p=0.58p=0.58. Which type of error was made?

  1. Type I error: rejecting a true null hypothesis
  2. No error was made because they used α=0.05\alpha=0.05
  3. Type II error: failing to reject a false null hypothesis (correct answer)
  4. Type II error: rejecting a true null hypothesis
  5. Type I error: failing to reject a false null hypothesis

Explanation: This question tests understanding of Type II errors in hypothesis testing. The health department failed to reject the null hypothesis (concluded no evidence of majority support) when in reality the null hypothesis was false (true proportion is 0.58, which exceeds 0.50). This is the definition of a Type II error: failing to reject a false null hypothesis. The p-value of 0.11 being greater than α = 0.05 led to failing to reject, missing the real majority support that exists. Type II errors in policy decisions can lead to missed opportunities when genuine public support exists but isn't detected by the test.

Question 16

An environmental agency tests whether the mean lead concentration in a river exceeds the legal limit of 15 ppb. They test H0:μ=15H_0: \mu=15 vs. Ha:μ>15H_a: \mu>15 using α=0.02\alpha=0.02. They fail to reject H0H_0 and conclude there is not convincing evidence the river exceeds the legal limit. In reality, the true mean is μ=18\mu=18 ppb. Which type of error was made?

  1. No error: failing to reject H0H_0 means the river is at 15 ppb
  2. Type I error: concluding the river exceeds the limit when it does not
  3. Type II error: failing to detect that the river exceeds the limit (correct answer)
  4. Type I error: failing to reject H0H_0 when μ>15\mu>15
  5. Type II error: concluding the river exceeds the limit when it does not

Explanation: This question tests understanding of Type II errors in environmental testing. The agency failed to reject H₀ (concluded no evidence the river exceeds the limit) when the alternative hypothesis is actually true (μ = 18 > 15, the river DOES exceed the limit). A Type II error occurs when we fail to reject a false null hypothesis - we miss detecting a real problem. This matches perfectly: the river actually exceeds the legal limit by 3 ppb, but the test failed to detect this violation. Type I errors involve rejecting a true H₀, which cannot happen when we fail to reject.

Question 17

A school tests whether a new tutoring program increases the proportion of students who pass an exam. They test H0:p=0.60H_0: p=0.60 vs. Ha:p>0.60H_a: p>0.60 at α=0.10\alpha=0.10. The result is p-value =0.07=0.07, so they reject H0H_0 and conclude the tutoring program increases the pass rate. In truth, the tutoring program does not change the pass rate and the true proportion is still p=0.60p=0.60. Which type of error was made?

  1. Type II error: failing to reject a false null hypothesis
  2. Type I error: rejecting a true null hypothesis (correct answer)
  3. No error was made because the conclusion matched the alternative hypothesis
  4. Type II error: rejecting a true null hypothesis
  5. Type I error: failing to reject a false null hypothesis

Explanation: This question tests understanding of Type I errors in hypothesis testing. The school rejected the null hypothesis (concluded the tutoring program increases pass rate) when in reality the null hypothesis was true (proportion is still 0.60). This is the definition of a Type I error: rejecting a true null hypothesis. The p-value of 0.07 being less than α = 0.10 led to rejection, but since the true proportion remained 0.60, this rejection was incorrect. Type I errors are controlled by the significance level α, which in this case was set at a relatively high 0.10, increasing the chance of this false positive result.

Question 18

An online retailer tests whether the proportion of customers who complete checkout after adding an item to the cart is different from 0.40. They test H0:p=0.40H_0: p=0.40 versus Ha:p≠0.40H_a: p\neq 0.40 at α=0.05\alpha=0.05. The test is statistically significant, so they conclude the completion rate is different from 0.40 and roll out a new checkout design. In reality, the true population proportion with the new design is p=0.40p=0.40. Which type of error was made?

  1. Type II error (failing to reject a false null hypothesis)
  2. No error was made because a two-sided test prevents errors
  3. Type I error (rejecting a true null hypothesis) (correct answer)
  4. Type I error (failing to reject a false null hypothesis)
  5. Type II error (rejecting a true null hypothesis)

Explanation: This question presents a Type I error with a two-sided test. The retailer rejected the null hypothesis (concluded p ≠ 0.40) when the null hypothesis was actually true (p = 0.40). This is a Type I error - rejecting a true null hypothesis. The statistically significant result led to implementing a new design that didn't actually change the completion rate. Two-sided tests can produce Type I errors in either direction, but the error type depends only on whether H₀ was true, not on the direction of the alternative. Students should understand that Type I errors represent false discoveries where we claim a difference exists when it doesn't, potentially leading to unnecessary changes or interventions.

Question 19

A school district tests whether a new tutoring program changes the mean math score from the historical mean of 75. The hypotheses are H0:μ=75H_0: \mu = 75 and Ha:μ≠75H_a: \mu \ne 75. At α=0.01\alpha = 0.01, the district rejects H0H_0. However, in the full population, the true mean score with the program is still μ=75\mu = 75. Which type of error was made?

  1. Type II error (failing to reject a false null hypothesis)
  2. No error was made because a small α\alpha prevents errors
  3. Type I error (rejecting a true null hypothesis) (correct answer)
  4. Type II error (rejecting a true null hypothesis)
  5. Type I error (failing to reject a false null hypothesis)

Explanation: This question evaluates the understanding of potential errors in performing hypothesis tests, focusing on Type I and Type II in AP Statistics. The decision was to reject H0 (μ = 75), but in reality μ = 75, so H0 is true. Thus, rejecting a true null hypothesis is a Type I error. A common distractor is choice A, which describes Type II error correctly but applies it wrongly since H0 was rejected, not failed to reject. Another distractor is choice E, which mislabels the description of Type II as Type I. For a mini-lesson, Type I error is like a false alarm (rejecting true H0), with probability α, while Type II is missing the signal (failing to reject false H0); in two-sided tests, the alternative covers both directions, making errors based strictly on H0's truth.

Question 20

A manufacturer tests whether the proportion of defective parts exceeds 2%. The hypotheses are H0:p=0.02H_0: p = 0.02 and Ha:p>0.02H_a: p > 0.02. After sampling, the company fails to reject H0H_0 at α=0.05\alpha = 0.05. In reality, the true defect rate is p=0.02p = 0.02. Which type of error was made?

  1. Type I error (rejecting a true null hypothesis)
  2. Type II error (failing to reject a false null hypothesis)
  3. Type II error (rejecting a true null hypothesis)
  4. No error was made (correct answer)
  5. Type I error (failing to reject a false null hypothesis)

Explanation: This question tests the skill of recognizing when no error occurs in hypothesis testing, alongside Type I and Type II errors. The decision was to fail to reject H0 (p = 0.02), and in reality p = 0.02, so H0 is true, meaning the correct decision was made with no error. Choice D correctly identifies this as no error. A common distractor is choice B, which claims Type II error but misapplies it since H0 is true, not false. Another distractor is choice A, which has the correct Type II description but doesn't fit because the decision matches reality. In a mini-lesson, no error happens when the decision aligns with the truth: failing to reject true H0 or rejecting false H0; Type I is rejecting true H0, and Type II is failing to reject false H0.