Quackers conducted his first study! His p-value is .027. What can he conclude?

Question

BlackTom AI · Accepted Answer

A p-value of 0.027 means the probability of observing data as extreme as (or more extreme than) what Quackers observed, assuming the null hypothesis is true, is 2.7%.

1) Relevant knowledge points and concepts
- Definition of p-value: p = P(observed result or more extreme | H0 true). It is a conditional probability given the null hypothesis.
- Significance levels (α): commonly 0.05; if p < α, we reject H0.
- Distinctions: p-value is not P(H0 true), not the probability the result was “due to chance” in a causal sense, and not the probability of a Type II error (β).

2) Step-by-step reasoning
- Quackers obtained p = 0.027. Convert to percent: 0.027 × 100% = 2.7%.
- Interpret using the p-value definition: this 2.7% quantifies how surprising the observed data are under H0.
- Compare to a typical α (for decision-making): 0.027 < 0.05, so under a 5% threshold one would reject H0. The interpretation remains the same regardless of α: the p-value itself is the conditional probability described above.

3) Intermediate/calculation steps
- p = 0.027
- Percent form: 0.027 × 100 = 2.7%
- Decision comparison: 0.027 < 0.05 → reject H0 at α = 0.05 (if a decision is required)

4) Why the correct answer is correct
- The first option exactly states the formal definition of a p-value: “The probability of seeing that data or more extreme if the null hypothesis is true is 2.7%.” This is precisely what p = 0.027 conveys.

5) Why the other options are incorrect
- “The probability that the result was due to chance is 2.7%”: vague/ambiguous causal language; p-value does not quantify the probability the observed effect was caused by chance versus a real effect.
- “The probability that the null hypothesis is true is 2.7%”: incorrect; p-value is not P(H0 true). That would require Bayesian posterior probability.
- “The probability of a Type 2 error is 2.7%”: Type II error (β) is the probability of failing to reject a false H0; unrelated to the p-value.
- “The probability that Quackers is the Best Duck Ever is 2.7%”: humorous and not a statistical interpretation.

6) Conclusion
The correct interpretation is the first option: The probability of seeing that data or more extreme if the null hypothesis is true is 2.7%, which matches the proper meaning of p = 0.027.

Quackers conducted his first study! His p-value is .027. What can he conclude?单项选择题

类似问题

Quackers conducted his first study! His p-value is .063. What can he conclude?

Statistical tests such as a t-test generate a p-value. The p-value is best described as the probability of which of the following?

What does a p-value of 0.85 mean?

这句话是真还是假？ “所有假设检验中，符号感值必须达到0.05，以确保实验间的一致性。”

True or False: The p-value represents the probability that you will correctly reject the null hypothesis when it is truly incorrect. (Assume no other sources of the following: bias, confounding, effect modification or measurement error)

What does a p-value represent in hypothesis testing?

Finding a small value of the p-value (e.g. less than 5%)

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