For this reason, choosing a lower significance level means that you can have more confidence in your decision to reject a null hypothesis. Remember, however, that the lower the p-value, the stronger the evidence is in support of the alternative hypothesis. You could just as easily use a significance level of 0.1 or 0.01, for example. The most commonly used significance level is 0.05 or 5%, but the choice of the significance level is up to the researcher. This threshold is known as the significance level (or alpha level) of the test.
When the p-value is below a certain threshold, the null hypothesis is rejected in favor of the alternative hypothesis. Reject or Fail to Reject the Null Hypothesis? The closer the p-value is to zero, the stronger the evidence is in support of the alternative hypothesis, H a H_a H a . The p-value can be used in the final stage of the test to make this determination.īecause it is a probability, the p-value can be expressed as a decimal or a percentage ranging from 0 to 1 or 0% to 100%. The goal of a hypothesis test is to use statistical evidence from a sample or multiple samples to determine which of the hypotheses is more likely to be true. In a hypothesis test, you have two competing hypotheses: a null (or starting) hypothesis, H 0 H_0 H 0 and an alternative hypothesis, H a H_a H a . It represents the probability of observing sample data that is at least as extreme as the observed sample data, assuming that the null hypothesis is true. The critical z can be calculated with the =NORM.S.INV function and the p-value with the =NORM.S.Calculating p-Values for Discrete Random VariablesĬalculating p-Values for Continuous Random VariablesĪ p-value (short for probability value) is a probability used in hypothesis testing. The p-value means that there is approximately 7.11% chance that we would get at least as extreme a test statistic as the one we had at 0.42 assuming that the true proportion is 0.35. We get a p-value of 0.0711 which is greater than our 0.05 alpha which also leads to the conclusion of failing to reject H0. The test does not give evidence to support the alternative hypothesis and we therefore do not have ground to say that the population proportion is larger than 0.35. Our z-score, or our sample statistics, is 1.4676 which is less this than the critical z if 1.96, so we fail to reject the null hypothesis. The z-score is calculated by subtracting the assumed proportion from the sample estimate divided by the standard error of the assumed proportion (the one under the null hypothesis): Also, we would usually work with larger sample sizes to work with proportions in the first place. Second step is to set the significance level (α): We will set it to 0.05, which means that there is a 5% risk that we will reject a correct null hypothesis:įor proportions we can calculate the standard deviation (σ) and we therefore apply the standard normal table. The alternative hypothesis states that the mean proportion is greater than 0.35 as we have had a sample proportion of 0.42. The null hypothesis will then state that the proportion is maximum 0.35 despite the new finding of 0.42. In our voting example, say we wish to test if the proportion mean is greater than the assumed 0.35. Our null hypothesis states that there is no change.
Let’s test it proportion hypothesis testing: Is this new finding of the 42% significant and can the proportion mean therefore be expected to be larger than the assumed 0.35? It is predicted that candidate C will get 35% of the votes, but running a sample survey of 100 voters, Candidate C becomes 42% of the predicted votes. I will use the following example to run through the procedure:Ī larger organization is due to elect a new board member. The procedure is for proportion hypothesis testing is the same as described in hypothesis testing: Procedure for proportion hypothesis testing