Question

My factory makes thermometers and I am testing if they are accurate. I will test this by measuring the average temperatures of different thermometers in ice-water. The null hypothesis is that the true average reading of thermometers from this factory in ice-water is 0◦ against the two-sided alternative. I will construct a p-value. What will the value of the p-value mean? If you wish, you can pretend the value of the p-value will be 0.06.

Answer 1

When you perform a hypothesis test in statistics, a p-value helps you determine the significance of your results. Hypothesis tests are used to test the validity of a claim that is made about a population. This claim that’s on trial, in essence, is called the null hypothesis.

The alternative hypothesis is the one you would believe if the null hypothesis is concluded to be untrue. The evidence in the trial is your data and the statistics that go along with it. All hypothesis tests ultimately use a p-value to weigh the strength of the evidence (what the data are telling you about the population). The p-value is a number between 0 and 1 and interpreted in the following way:

The P value, or calculated probability, is the probability of finding the observed, or more extreme, results when the null hypothesis (H₀) of a study question is true – the definition of ‘extreme’ depends on how the hypothesis is being tested.

• A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.

• A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.

• p-values very close to the cutoff (0.05) are considered to be marginal (could go either way). Always report the p-value so your readers can draw their own conclusions.