Probability, Statistics and Queueing
Which of the following correctly describes the meaning of the p-value obtained in a hypothesis test?
- AThe probability, calculated from the observed data, that the null hypothesis itself is true
- BIf the p-value is 0.03, the probability that the alternative hypothesis is true is 97%
- CThe probability, assuming the null hypothesis is true, of obtaining the observed result or a more extreme one
Show answer and explanation
Answer: C. The probability, assuming the null hypothesis is true, of obtaining the observed result or a more extreme one
A hypothesis test sets up a null hypothesis such as "there is no difference" and uses the p-value to express how unlikely a result like the actual data would be if it were true. If the p-value is smaller than a significance level decided in advance (for example 0.05), the null hypothesis is rejected and a difference is judged to exist. The p-value is not the probability that the null or the alternative hypothesis itself is true.
- A. The p-value is calculated assuming the null hypothesis is true; it is not the probability that the null hypothesis is true.
- B. Subtracting the p-value from 1 does not give the probability that the alternative hypothesis is true.
- C. Correct. It is the probability, under the null hypothesis, of a result equal to or more extreme than the one observed.
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