Question

In a hypothesis test, the pValue tells us

Answer 1

The P-value approach involves determining "likely" or "unlikely" by determining the probability — assuming the null hypothesis were true — of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed. If the P-value is small, say less than (or equal to) αα, then it is "unlikely." And, if the P-value is large, say more than α, then it is "likely."

If the P-value is less than (or equal to) α, then the null hypothesis is rejected in favor of the alternative hypothesis. And, if the P-value is greater than α, then the null hypothesis is not rejected.

Specifically, the four steps involved in using the P-value approach to conducting any hypothesis test are:

1. Specify the null and alternative hypotheses.
2. Using the sample data and assuming the null hypothesis is true, calculate the value of the test statistic. Again, to conduct the hypothesis test for the population mean μ, we use the t-statistic which follows a t-distribution with n - 1 degrees of freedom.
3. Using the known distribution of the test statistic, calculate the P-value: "If the null hypothesis is true, what is the probability that we'd observe a more extreme test statistic in the direction of the alternative hypothesis than we did?" (Note how this question is equivalent to the question answered in criminal trials: "If the defendant is innocent, what is the chance that we'd observe such extreme criminal evidence?")
4. Set the significance level, αα, the probability of making a Type I error to be small — 0.01, 0.05, or 0.10. Compare the P-value to α. If the P-value is less than (or equal to) α, reject the null hypothesis in favor of the alternative hypothesis. If the P-value is greater than α, do not reject the null hypothesis.