College Statistics Quiz: Type I And Type Ii Errors
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Type I And Type Ii ErrorsQuestion 1 of 20

A researcher performs a hypothesis test and decides to change the significance level α from 0.05 to 0.01. Assuming the sample size and the true mean remain the same, what is the definitive consequence for the probability of a Type II error (β) and the power of the test (1 - β)?

β will decrease and power will increase.
β will increase and power will decrease.
β will be unaffected, but power will decrease.
Both β and power will remain unchanged because the data have not changed.
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College Statistics Quiz

College Statistics Quiz: Type I And Type Ii Errors

Practice Type I And Type Ii Errors in College 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 Type I And Type Ii Errors, giving you a quick way to practice the rules, question types, and explanations that matter most for College 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 researcher performs a hypothesis test and decides to change the significance level α from 0.05 to 0.01. Assuming the sample size and the true mean remain the same, what is the definitive consequence for the probability of a Type II error (β) and the power of the test (1 - β)?

  1. β will decrease and power will increase.
  2. β will increase and power will decrease. (correct answer)
  3. β will be unaffected, but power will decrease.
  4. Both β and power will remain unchanged because the data have not changed.
Explanation: There is an inverse relationship between α and β. Decreasing α (from 0.05 to 0.01) makes the rejection criteria more stringent. This means it is harder to reject the null hypothesis. This reduces the probability of a Type I error (α) but increases the probability of failing to reject a false null hypothesis (β). Since power is defined as 1 - β, an increase in β leads to a decrease in power.

Question 2

A study is designed to test H₀: μ = 50 versus Hₐ: μ > 50 with α = 0.05 and a sample of size n = 100. Researchers determine that if the true mean is actually μ = 52, the power of the test is 0.64. If, however, the true mean is actually μ = 54, what can be concluded about the power of the test?

  1. The power will be less than 0.64.
  2. The relationship cannot be determined without knowing the p-value.
  3. The power will remain 0.64 because α and n are fixed.
  4. The power will be greater than 0.64. (correct answer)
Explanation: When you encounter questions about statistical power, remember that power is the probability of correctly rejecting a false null hypothesis. Power increases as the true parameter value moves further from the null hypothesis value in the direction of the alternative hypothesis. In this one-tailed test with H0:μ=50H_0: μ = 50 versus Ha:μ>50H_a: μ > 50, you're given that when the true mean is μ=52μ = 52, the power is 0.64. If the true mean is actually μ=54μ = 54, this represents a larger effect size—the true parameter is now 4 units away from the null value instead of just 2 units. As the true mean moves further into the alternative hypothesis region (greater than 50), it becomes easier to detect this difference, increasing the probability of correctly rejecting the false null hypothesis. Choice A is incorrect because power increases, not decreases, with larger effect sizes. Choice B misunderstands the relationship—power depends on the effect size and other test parameters, not on p-values from individual samples. Choice C reflects a common misconception that power is fixed when α and n are constant. While these factors do influence power, the effect size (difference between true and hypothesized values) is equally important in determining power. The answer is D: the power will be greater than 0.64. Study tip: Remember that power always increases as the true parameter moves further from the null hypothesis value in the direction specified by the alternative hypothesis. Visualize the power curve—it's steepest near the null value and approaches 1 as effect size increases.

Question 3

For a hypothesis test with a fixed sample size and a fixed, non-zero effect size, consider a graph where the probability of a Type II error (β) is on the y-axis and the probability of a Type I error (α) is on the x-axis. As α is allowed to vary from 0 to 1, which of the following best describes the shape of the resulting curve?

  1. A strictly decreasing curve, showing the trade-off between the two error types. (correct answer)
  2. A strictly increasing curve, showing that as α increases, β also increases.
  3. A U-shaped curve, indicating that β is minimized for a moderate value of α.
  4. A horizontal line, indicating that β is independent of the choice of α.
Explanation: When you encounter questions about Type I and Type II errors, focus on the fundamental relationship between these error types. Type I error (α) is rejecting a true null hypothesis, while Type II error (β) is failing to reject a false null hypothesis. The key insight is that α and β have an inverse relationship when sample size and effect size are fixed. As you make your test more stringent by decreasing α (requiring stronger evidence to reject the null), you simultaneously make it harder to detect a true effect, thus increasing β. Conversely, as you increase α (making it easier to reject the null), you become more likely to detect a true effect when one exists, decreasing β. This creates a strictly decreasing curve where β decreases as α increases - exactly what option A describes. The relationship isn't linear, but it's monotonically decreasing. Option B incorrectly suggests both error types increase together, which contradicts their inverse relationship. Option C proposes a U-shaped curve implying β could be minimized at some moderate α value, but this isn't true - β continues decreasing as α increases (though with diminishing returns). Option D suggests independence between the errors, which ignores the fundamental trade-off that defines hypothesis testing. Remember this core principle: with fixed sample size and effect size, you cannot simultaneously minimize both error types. This trade-off is why choosing an appropriate significance level (typically 0.05) involves balancing the costs of each error type for your specific situation.

Question 4

A clinical trial for a new cancer therapy is conducted with the null hypothesis that the therapy has no effect on patient survival rates. Which of the two error types is generally considered to have more severe human consequences, and how should this influence the choice of significance level α?

  1. Type I error is more severe; α should be set to a very low value (e.g., 0.01).
  2. Type I error is more severe; α should be set to a relatively high value (e.g., 0.10).
  3. Type II error is more severe; α should be set to a relatively high value (e.g., 0.10). (correct answer)
  4. Type II error is more severe; α should be set to a very low value (e.g., 0.01).
Explanation: When evaluating clinical trials, understanding the real-world consequences of statistical errors is crucial for making ethical decisions about significance levels. In this cancer therapy trial, a Type I error means rejecting a true null hypothesis—concluding the therapy works when it actually doesn't. A Type II error means failing to reject a false null hypothesis—concluding the therapy doesn't work when it actually does. From a human perspective, a Type II error is far more severe because it means withholding a potentially life-saving treatment from cancer patients who could benefit. To minimize Type II errors, you need to increase statistical power, which means being more willing to detect effects when they exist. This requires setting a higher significance level (like α=0.10α = 0.10) rather than a very conservative one. A higher α makes it easier to reject the null hypothesis, reducing the chance of missing a beneficial treatment. Answer A incorrectly identifies Type I error as more severe—while approving an ineffective treatment has consequences, it's generally less catastrophic than missing a cure. Answer B correctly identifies Type II as more problematic but suggests the wrong α direction. Answer D makes the critical error of recommending a very low α, which would actually increase Type II error risk by making it harder to detect real treatment effects. Remember this pattern: in medical contexts where missing a beneficial treatment has severe consequences (like cancer, heart disease), researchers often accept higher Type I error risk to minimize Type II errors. The stakes determine your statistical strategy.

Question 5

A clinical trial for a new cancer therapy is conducted with the null hypothesis that the therapy has no effect on patient survival rates. Which of the two error types is generally considered to have more severe human consequences, and how should this influence the choice of significance level α?

  1. Type I error is more severe; α should be set to a very low value (e.g., 0.01).
  2. Type I error is more severe; α should be set to a relatively high value (e.g., 0.10).
  3. Type II error is more severe; α should be set to a relatively high value (e.g., 0.10). (correct answer)
  4. Type II error is more severe; α should be set to a very low value (e.g., 0.01).
Explanation: When evaluating clinical trials, understanding the real-world consequences of statistical errors is crucial for making ethical decisions about significance levels. In this cancer therapy trial, a Type I error means rejecting a true null hypothesis—concluding the therapy works when it actually doesn't. A Type II error means failing to reject a false null hypothesis—concluding the therapy doesn't work when it actually does. From a human perspective, a Type II error is far more severe because it means withholding a potentially life-saving treatment from cancer patients who could benefit. To minimize Type II errors, you need to increase statistical power, which means being more willing to detect effects when they exist. This requires setting a higher significance level (like α=0.10α = 0.10) rather than a very conservative one. A higher α makes it easier to reject the null hypothesis, reducing the chance of missing a beneficial treatment. Answer A incorrectly identifies Type I error as more severe—while approving an ineffective treatment has consequences, it's generally less catastrophic than missing a cure. Answer B correctly identifies Type II as more problematic but suggests the wrong α direction. Answer D makes the critical error of recommending a very low α, which would actually increase Type II error risk by making it harder to detect real treatment effects. Remember this pattern: in medical contexts where missing a beneficial treatment has severe consequences (like cancer, heart disease), researchers often accept higher Type I error risk to minimize Type II errors. The stakes determine your statistical strategy.

Question 6

A study is designed to test H₀: μ = 50 versus Hₐ: μ > 50 with α = 0.05 and a sample of size n = 100. Researchers determine that if the true mean is actually μ = 52, the power of the test is 0.64. If, however, the true mean is actually μ = 54, what can be concluded about the power of the test?

  1. The power will be less than 0.64.
  2. The relationship cannot be determined without knowing the p-value.
  3. The power will remain 0.64 because α and n are fixed.
  4. The power will be greater than 0.64. (correct answer)
Explanation: When you encounter questions about statistical power, remember that power is the probability of correctly rejecting a false null hypothesis. Power increases as the true parameter value moves further from the null hypothesis value in the direction of the alternative hypothesis. In this one-tailed test with H0:μ=50H_0: μ = 50 versus Ha:μ>50H_a: μ > 50, you're given that when the true mean is μ=52μ = 52, the power is 0.64. If the true mean is actually μ=54μ = 54, this represents a larger effect size—the true parameter is now 4 units away from the null value instead of just 2 units. As the true mean moves further into the alternative hypothesis region (greater than 50), it becomes easier to detect this difference, increasing the probability of correctly rejecting the false null hypothesis. Choice A is incorrect because power increases, not decreases, with larger effect sizes. Choice B misunderstands the relationship—power depends on the effect size and other test parameters, not on p-values from individual samples. Choice C reflects a common misconception that power is fixed when α and n are constant. While these factors do influence power, the effect size (difference between true and hypothesized values) is equally important in determining power. The answer is D: the power will be greater than 0.64. Study tip: Remember that power always increases as the true parameter moves further from the null hypothesis value in the direction specified by the alternative hypothesis. Visualize the power curve—it's steepest near the null value and approaches 1 as effect size increases.

Question 7

A research team is conducting a hypothesis test where the consequences of a Type I error are judged to be far more severe than the consequences of a Type II error (e.g., approving a harmful new drug). Which of the following represents the most appropriate strategy for designing their test?

  1. Set a very low significance level (e.g., α = 0.001) to minimize the chance of incorrectly rejecting the null hypothesis. (correct answer)
  2. Set a high significance level (e.g., α = 0.10) to maximize the power of the test to detect a true effect.
  3. Use the smallest possible sample size to reduce the costs and complexity of the experiment.
  4. Ensure the probability of a Type II error (β) is as close to zero as possible, even if it means increasing α.
Explanation: The probability of a Type I error is denoted by the significance level, α. If a Type I error is very costly, the researcher should make its probability as low as possible. Choosing a very small α (like 0.001) directly reduces the risk of committing this type of error. While this will increase the probability of a Type II error (β), the question states that this is the less severe error.

Question 8

A political campaign wants to test if a new ad series has increased a candidate's approval rating above 40%. The null hypothesis is H₀: p ≤ 0.40. The campaign is concerned about failing to detect a genuine increase in approval. To address this, they wish to reduce the probability of a Type II error without changing the pre-specified significance level (α). Which action would achieve this?

  1. Lowering the significance level from α = 0.05 to α = 0.01.
  2. Decreasing the number of voters surveyed to streamline the polling process.
  3. Increasing the number of voters surveyed for the poll. (correct answer)
  4. Changing the alternative hypothesis to be two-sided (Hₐ: p ≠ 0.40).
Explanation: The probability of a Type II error (β) is reduced by increasing the power of the test. The three main factors that increase power are increasing the significance level (α), increasing the effect size, or increasing the sample size (n). Since the campaign cannot change α or the true effect size, the only action they can take is to increase the sample size. A larger sample provides more information and makes it easier to detect a true effect.

Question 9

A pharmaceutical company develops a new drug to treat a rare, life-threatening disease for which the current treatment has severe side effects. The company conducts a clinical trial to test the new drug's efficacy. The null hypothesis is that the new drug is no more effective than the current treatment. If a Type I error is committed during this trial, what is the most direct and significant consequence?

  1. The company will incorrectly conclude the drug is no better than the old treatment and will abandon a potentially effective medication.
  2. The new drug, which is no more effective than the current treatment, will be approved and marketed, potentially exposing patients to new risks without benefit. (correct answer)
  3. The company will correctly conclude the new drug is more effective and will replace the old treatment, benefiting patients.
  4. The trial will correctly determine that the new drug is not an improvement, saving the company from further development costs.
Explanation: A Type I error is the rejection of a true null hypothesis. In this context, the null hypothesis (H₀) is that the new drug is no more effective. Rejecting H₀ means concluding the new drug is more effective. If this is an error, it means the new drug is actually not an improvement. Therefore, the consequence is marketing a new drug that is no better than the old one, which could expose patients to unknown side effects for no additional therapeutic benefit.

Question 10

A factory's wastewater is tested to determine if the mean concentration of a pollutant exceeds the legally permissible limit of 100 parts per million (ppm). The regulatory agency sets up the hypotheses as H₀: μ ≤ 100 versus Hₐ: μ > 100. After analyzing water samples, the agency fails to reject the null hypothesis. If, in fact, the factory's mean pollutant level is 115 ppm, which error has been made and what is the consequence?

  1. A Type I error occurred, leading to the factory being unfairly penalized even though it was complying with the law.
  2. A Type II error occurred, allowing the factory to continue polluting the environment at illegally high levels. (correct answer)
  3. A Type I error occurred, allowing the factory to continue polluting because the agency failed to detect the violation.
  4. A Type II error occurred, resulting in the factory being wrongly accused of pollution and facing unnecessary fines.
Explanation: A Type II error is failing to reject a false null hypothesis. Here, the agency failed to reject H₀ (μ ≤ 100). However, the reality is that the null hypothesis is false (μ = 115 ppm). This is a Type II error. The consequence is that the violation is not detected, and the factory continues to release excessive pollutants.

Question 11

In a hypothesis test of H₀: μ = 10 against Hₐ: μ ≠ 10, a p-value of 0.12 is obtained from a sample. A researcher using a significance level of α = 0.05 fails to reject H₀. Which of the following statements correctly describes the situation?

  1. The researcher has proven that the true mean is 10, so no error could have been made.
  2. The researcher has failed to find sufficient evidence that the true mean is not 10, and it is possible a Type II error was committed. (correct answer)
  3. The researcher has failed to find sufficient evidence that the true mean is not 10, and it is possible a Type I error was committed.
  4. If the researcher had used α = 0.15, they would have rejected the null hypothesis and made a Type I error.
Explanation: Since the p-value (0.12) is greater than α (0.05), the correct decision is to fail to reject H₀. When we fail to reject H₀, we never prove H₀ is true; we only conclude there is insufficient evidence against it. The only type of error that can be made in this situation is a Type II error, which occurs if we fail to reject H₀ when it is actually false.

Question 12

In the American legal system, a defendant is presumed innocent until proven guilty. This corresponds to a hypothesis test where H₀: The defendant is innocent, and Hₐ: The defendant is guilty. The standard of "beyond a reasonable doubt" relates to the significance level. What does a Type II error represent in this context?

  1. Convicting an innocent person.
  2. Acquitting a guilty person. (correct answer)
  3. Convicting a guilty person.
  4. Acquitting an innocent person.
Explanation: A Type II error is the failure to reject a false null hypothesis. In this analogy, the null hypothesis is innocence. If the null hypothesis is false, the defendant is actually guilty. Failing to reject H₀ means the jury does not find the defendant guilty, leading to an acquittal. Therefore, a Type II error is acquitting a person who is actually guilty.

Question 13

A 99% confidence interval for the difference between two population means (μ₁ - μ₂) is calculated to be (2.5, 8.3). If a hypothesis test were conducted for H₀: μ₁ - μ₂ = 0 versus Hₐ: μ₁ - μ₂ ≠ 0 using the same data, what would be the test's conclusion at the corresponding significance level, and what type of error could have been made?

  1. Reject H₀; a Type I error may have occurred. (correct answer)
  2. Fail to reject H₀; a Type II error may have occurred.
  3. Reject H₀; a Type II error may have occurred.
  4. Fail to reject H₀; a Type I error may have occurred.
Explanation: A 99% confidence interval corresponds to a hypothesis test at a significance level of α = 1 - 0.99 = 0.01. The null hypothesis H₀ states that the difference between the means is 0. Since the calculated confidence interval (2.5, 8.3) does not contain 0, the null hypothesis would be rejected. When the null hypothesis is rejected, it is possible that it was actually true, which means a Type I error may have occurred.

Question 14

A company claims its new breakfast cereal contains 'at most 10 grams of sugar per serving'. A consumer advocacy group plans to test this claim, believing the sugar content is higher. They set up hypotheses H₀: μ ≤ 10 and Hₐ: μ > 10. For the consumer group, what would be the consequence of making a Type II error?

  1. The group incorrectly concludes the cereal has more than 10g of sugar when it does not.
  2. The group fails to find evidence that the cereal has more than 10g of sugar when, in fact, it does. (correct answer)
  3. The group correctly identifies that the cereal has more than 10g of sugar, leading to a recall.
  4. The group confirms the company's claim is true, when it is indeed true.
Explanation: A Type II error is failing to reject a false null hypothesis. The null hypothesis (H₀) is that the mean sugar content is at most 10g (μ ≤ 10). If this is false, it means the true mean sugar content is greater than 10g (μ > 10). Failing to reject H₀ means the consumer group does not find sufficient evidence to challenge the company's claim. Therefore, a Type II error means the group fails to detect that the cereal's sugar content is higher than advertised.

Question 15

A researcher plans a study to test if a new teaching method improves test scores from the current mean of 75. The researcher is certain the new method will not worsen scores and decides to use a one-tailed test (Hₐ: μ > 75) instead of a two-tailed test (Hₐ: μ ≠ 75), keeping α and the sample size the same. How does this choice affect the power of the test to detect a true mean score of, for example, 80?

  1. The one-tailed test will have less power because it does not consider the possibility that μ < 75.
  2. The change in power cannot be determined without knowing the population standard deviation.
  3. The power will be identical for both tests because α, the effect size, and the sample size are the same.
  4. The one-tailed test will have more power because the entire rejection region is placed in the upper tail. (correct answer)
Explanation: When comparing one-tailed and two-tailed hypothesis tests, the key insight is understanding how the rejection region affects your ability to detect true effects. Statistical power is the probability of correctly rejecting a false null hypothesis, and it's directly influenced by how you allocate your critical region. In a two-tailed test with Ha:μ≠75H_a: \mu \neq 75, you split your significance level α\alpha between both tails (α/2\alpha/2 in each tail). For a one-tailed test with Ha:μ>75H_a: \mu > 75, you place the entire α\alpha in the upper tail. This means the critical value for the one-tailed test is less extreme than for the two-tailed test, making it easier to reject the null hypothesis when the true mean is indeed greater than 75. Since the researcher is testing whether the true mean is 80 (which is greater than 75), the one-tailed test concentrates all its "rejection power" exactly where the effect is expected to occur. This increases the probability of detecting the difference. Choice A is wrong because not considering μ<75\mu < 75 doesn't reduce power when testing for μ>75\mu > 75—it actually helps by focusing the test. Choice B is incorrect because power comparisons between these tests don't require knowing the population standard deviation; the relationship holds regardless. Choice C misses the crucial point that while the total α\alpha is the same, its distribution across tails differs, directly affecting power. Study tip: Remember that one-tailed tests always have more power than two-tailed tests when testing in the correct direction, because you're concentrating your entire α\alpha where you expect to find the effect.

Question 16

An experiment with a fixed sample size yields a p-value of 0.055 for a test of H₀: μ = 30 versus Hₐ: μ > 30. The researcher had set the significance level α = 0.05. The researcher is concerned that a small but important effect might actually exist. Which of the following is the most statistically sound explanation for the failure to find a significant result?

  1. The significance level α was set too high, making it too difficult to reject the null hypothesis.
  2. A Type I error must have occurred, masking the true effect of the experiment.
  3. The study may have been underpowered, possibly due to an insufficient sample size to detect the small effect. (correct answer)
  4. The result proves that the null hypothesis is true and that no effect exists.
Explanation: A p-value (0.055) that is very close to the significance level (0.05) suggests that there might be a real effect, but the evidence was not quite strong enough to be declared statistically significant. A common reason for this is low statistical power. The study may not have had a large enough sample size to reliably detect the true effect, leading to a potential Type II error. This is a more plausible explanation than the others.

Question 17

A quality control engineer at a bottling plant tests H₀: μ = 12 ounces versus Hₐ: μ ≠ 12 ounces for the mean volume of filled bottles. A Type I error occurs if the engineer concludes that the mean volume is...

  1. not equal to 12 ounces when, in fact, it is 12 ounces. (correct answer)
  2. equal to 12 ounces when, in fact, it is not 12 ounces.
  3. not equal to 12 ounces when, in fact, it is not 12 ounces.
  4. equal to 12 ounces when, in fact, it is 12 ounces.
Explanation: When you encounter hypothesis testing questions, focus on the precise definitions of Type I and Type II errors. A Type I error occurs when you reject a true null hypothesis, while a Type II error occurs when you fail to reject a false null hypothesis. In this bottling plant scenario, the null hypothesis states that the mean volume equals 12 ounces (H₀: μ = 12). The alternative hypothesis claims it doesn't equal 12 ounces (Hₐ: μ ≠ 12). A Type I error happens when you reject H₀ when it's actually true. This means concluding the mean volume is not equal to 12 ounces when it actually is 12 ounces. Answer A correctly describes this scenario: concluding the mean is not equal to 12 ounces when it actually is 12 ounces. This is exactly what happens in a Type I error. Answer B describes a Type II error instead—failing to reject a false null hypothesis. Here, you'd conclude the mean equals 12 ounces when it actually doesn't. Answer C represents a correct decision, not an error. If the mean truly isn't 12 ounces and you conclude it's not 12 ounces, you've made the right call. Answer D also represents a correct decision. If the mean truly is 12 ounces and you conclude it is 12 ounces, you've correctly failed to reject a true null hypothesis. Study tip: Remember "Type I = reject when true." Create a mental connection between Type I errors and false alarms—you're detecting a problem that doesn't actually exist, just like a smoke detector going off when there's no fire.

Question 18

A factory's wastewater is tested to determine if the mean concentration of a pollutant exceeds the legally permissible limit of 100 parts per million (ppm). The regulatory agency sets up the hypotheses as H₀: μ ≤ 100 versus Hₐ: μ > 100. After analyzing water samples, the agency fails to reject the null hypothesis. If, in fact, the factory's mean pollutant level is 115 ppm, which error has been made and what is the consequence?

  1. A Type I error occurred, leading to the factory being unfairly penalized even though it was complying with the law.
  2. A Type II error occurred, allowing the factory to continue polluting the environment at illegally high levels. (correct answer)
  3. A Type I error occurred, allowing the factory to continue polluting because the agency failed to detect the violation.
  4. A Type II error occurred, resulting in the factory being wrongly accused of pollution and facing unnecessary fines.
Explanation: A Type II error is failing to reject a false null hypothesis. Here, the agency failed to reject H₀ (μ ≤ 100). However, the reality is that the null hypothesis is false (μ = 115 ppm). This is a Type II error. The consequence is that the violation is not detected, and the factory continues to release excessive pollutants.

Question 19

A political campaign wants to test if a new ad series has increased a candidate's approval rating above 40%. The null hypothesis is H₀: p ≤ 0.40. The campaign is concerned about failing to detect a genuine increase in approval. To address this, they wish to reduce the probability of a Type II error without changing the pre-specified significance level (α). Which action would achieve this?

  1. Lowering the significance level from α = 0.05 to α = 0.01.
  2. Decreasing the number of voters surveyed to streamline the polling process.
  3. Increasing the number of voters surveyed for the poll. (correct answer)
  4. Changing the alternative hypothesis to be two-sided (Hₐ: p ≠ 0.40).
Explanation: The probability of a Type II error (β) is reduced by increasing the power of the test. The three main factors that increase power are increasing the significance level (α), increasing the effect size, or increasing the sample size (n). Since the campaign cannot change α or the true effect size, the only action they can take is to increase the sample size. A larger sample provides more information and makes it easier to detect a true effect.

Question 20

In the American legal system, a defendant is presumed innocent until proven guilty. This corresponds to a hypothesis test where H₀: The defendant is innocent, and Hₐ: The defendant is guilty. The standard of "beyond a reasonable doubt" relates to the significance level. What does a Type II error represent in this context?

  1. Convicting an innocent person.
  2. Acquitting a guilty person. (correct answer)
  3. Convicting a guilty person.
  4. Acquitting an innocent person.
Explanation: A Type II error is the failure to reject a false null hypothesis. In this analogy, the null hypothesis is innocence. If the null hypothesis is false, the defendant is actually guilty. Failing to reject H₀ means the jury does not find the defendant guilty, leading to an acquittal. Therefore, a Type II error is acquitting a person who is actually guilty.