Which one is true?

Question

Which one is true?

BlackTom AI · Accepted Answer

In this question, we evaluate statements about hypothesis testing and error types.
Option A: 'None of the other three.' This claim would be true only if all the other options were false. However, we will see that at least one other option makes a correct statement, so this option is not accurate.
Option B: 'P(type 2 error) is bigger than P(type 1 error).' In general, the probability of a Type II error is not inherently larger than the probability of a Type I error; it depends on sample size, effect size, and the chosen significance level. Therefore, this blanket assertion is not a guaranteed truth and is usually context-dependent, making it incorrect as a universal statement.
Option C: 'P(type 1 error) is bigger than P(type 2 error).' Similar to B, there is no universal ordering between Type I and Type II error probabilities. Without specifying sample size, effect size, and alpha, you cannot assert that Type I error probability is larger. This statement misstates the relationship, so it is not universally true.
Option D: 'Significance tests only control type 1 error.' This is the core principle of classical hypothesis testing: the chosen significance level alpha (e.g., 0.05) directly controls the probability of incorrectly rejecting a true null hypothesis (Type I error). Type II error, on the other hand, relates to failing to reject a false null and depends on power, sample size, and true effect size; it is not controlled by alpha alone. This makes the statement a correct characterization of what significance tests control.
Thus, step by step, we see that only Option D presents a universally correct property of standard significance testing, while A, B, and C rely on assumptions that do not hold in general.

Which one is true?单项选择题

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