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

Question

BlackTom AI · Accepted Answer

Assuming the null hypothesis is true, a p-value of 0.063 means that the probability of observing data as extreme as (or more extreme than) what Quackers observed is 6.3%.

1) Relevant concepts
- Null hypothesis (H0): a statement of no effect; p-value is computed under H0.
- p-value definition: P(observed statistic or more extreme | H0 true).
- Significance level (α): a pre-specified cutoff (commonly 0.05) used to decide whether to reject H0.
- Common misunderstandings: p-value is not P(H0 true) and is not directly the Type I error probability unless α is set equal to the p-value.

2) Step-by-step reasoning
- Given p = 0.063 and typical α = 0.05, compare p to α: 0.063 > 0.05.
- Because p > α, you do not reject the null hypothesis at the 5% level.
- The p-value itself quantifies how unusual the data are under H0: here, such data would occur about 6.3% of the time if H0 were true.

3) Intermediate/calculation steps
- Numerical comparison: 0.063 (observed p) − 0.05 (common α) = 0.013 > 0, so do not reject H0 at α = 0.05.
- Interpretation alternative: the smallest α at which you would reject is 6.3% (i.e., α = 0.063); for any α ≤ 0.063 you would reject, for α < 0.063 you would not.

4) Why the correct answer is correct
- The correct option exactly matches the formal definition of a p-value: the probability of seeing the observed data or more extreme assuming the null hypothesis is true (6.3%).

5) Why the other options are incorrect
- "The probability that the result was due to chance is 6.3%": vague/misleading phrasing; p-value conditions on H0 and does not directly state “due to chance” in causal terms.
- "The probability that the null hypothesis is true is 6.3%": wrong—p-value is P(data|H0), not P(H0|data).
- "The probability of a Type 1 error is 6.3%": incorrect—Type I error rate is the chosen α, not the observed p-value (though p is the smallest α that would lead to rejection).
- "The probability that Quackers is the Best Duck Ever is 6.3%": irrelevant and not a statistical interpretation.

6) Conclusion
The correct interpretation is: "The probability of seeing that data or more extreme if the null is true is 6.3%," which matches the provided answer.

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

类似问题

Quackers conducted his first study! His p-value is .027. 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%)

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单