Question

Whether we are conducting a hypothesis test with regards to a one population parameter or two population parameters (usually the difference between two population parameters), the concept of p-value is extremely important in making a decision with respect to the null hypothesis. A very common mistake in elementary statistics is interpreting the p-value of a hypothesis test. Many students think that the p-value is the probability that the null hypothesis is true or that it is the probability of rejecting the null hypothesis:

• Explain why you think many students erroneously come to these conclusions.
• In your own words, explain what the p-value represents.
• What pages of the reading in OLI support your explanation? (ignore this question)

Answer 1

The conclusion is erroneous is because of the test statistic. The test statistic uses a value which is obtained from the null hypothesis (H0: p = value). Because of this null hypothesis, students erroneously think that the z value obtained gives us a probability which is related to either rejecting the null or the probability of the null hypothesis being true.

Some times the definition of the p value can lead to an erroneous conclusion because of the way it is worded.

The p value is defined as the probability of getting a value as extreme or greater than that obtained (that is, the value of the test statistic), assuming that the null hypothesis is true. A probability value less than the level of significance decided beforehand, helps us to make the decision of whether it is too low or too (to make the decision of rejecting the null hypothesis or fail to reject the null hypothesis respectively)