A Hypothesis test for a single proportion is used to see if a sample is reflective of the whole population or is a new proportion must be established for a known value. (Example)
- Can be used to compare a data set with a known value or null hypothesis.
- Used when a success/failure is easily applied to a single statistic.
There are 5 steps to the single proportion hypothesis test. First, a philosophical question has to be asked about what the statistician is attempting to show with the data, then a null and alternate hypothesis must be formed. The null hypothesis is either a known value or a hypothesized one. For example, they could be a cancer rate or a projected success rate in roulette. A good article on forming a hypothesis for single proportions can be found here.
Once the framework for the analysis is established, the statistician must check whether or not the data was random, that no more than 10% of the population was sampled, and they must check that the number of successes or failures times the the sample size (np^ and nq^) is greater than 10.
Next, we must calculate a test statistic, Z*. There is a good mathematical description in the link provided. The z score is used to show how confident we are that our data did not come about by mere chance, and it is used to find a P value.
We now use the test statistic to compare our data with the null hypothesis, and determine if we can reject or accept the null. One problem researchers tend to have with this method is using their hypothesized population values as the null hypothesis, and show that the data fails to reject the null, when it is not within the power of the test to show that the null is correct.
Finally, a conclusion based on the P value and alpha value can be made. In the end, there are two outcomes. We can reject the null or fail to reject the null.