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?

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For an upper-tail hypotheses about a population mean with σ known and α=5%, which one is the rejection region?

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Which one is true?

查看解析

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类似问题

For an upper-tail hypotheses about a population mean with σ known and α=5%, which one is the rejection region?

For a given sample, the P-value for upper tail test is x, and the P-value for two-tailed test is y, then

For a two-tailed hypothesis test with a test statistic value of z = 2.09, the p-value is _____.

For a sample size of 30, changing from using the t distribution to using the standard normal distribution in a hypothesis test _____.

Exhibit 9-5 n = 16 H0: μ ≥ 80 = 75.607 Ha: μ < 80 σ = 8.6 Assume the population is normally distributed. Refer to Exhibit 9-5. The p-value is equal to _____.

Exhibit 9-1 ​ ​ Refer to Exhibit 9-1. If the test is done at a .01 level of significance, the null hypothesis should _____.

What conclusion for a test would correctly detect a difference between the actual parameter and the hypothesized value for the parameter? c08.p089.q0008

Which of the following statements descrbes best the characteristics of the one-tailed and two-tailed tests in statistical hypothesis testing?

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Exhibit 9-1 Refer to Exhibit 9-1. If the test is done at a .01 level of significance, the null hypothesis should _____.