Hypothesis Testing

Inferential statistics is the process of employing hypothesis testing to random samples drawn from unknown population distribution to determine a targeted characteristic. The central limit theorem provides the foundation upon which it is possible to have confidence in the value of the point estimates subjected to hypothesis testing. 

Steps for a Hypothesis Test

1. State the null hypothesis.
2. State the alternative hypothesis.
3. Determine the critical value (based upon chosen type of distribution (normal or Student’s t) 
4. Determine if this will be a 1-tail or 2-tailed test (other another test). 
5. Calculate the test statistic. 
6. Draw a conclusion (inference) from the results. 

The process of hypothesis testing begins with the framing of two hypotheses from the research question – the null hypothesis and the alternative hypothesis.

H₀: The Null Hypothesis is an opposing statement to your proposed research question. The process of hypothesis testing is actually null hypothesis testing such that the results will allow you to either reject the null hypothesis or fail to reject the null hypothesis.  You will never use the results of a hypothesis to accept the null hypothesis. 

H_a: The Alternative Hypothesis is a direct statement drawn from your research question and it is basically the contradictory statement to the null hypothesis (H₀).  When you perform the hypothesis test, the result will be used to either reject the null hypothesis or fail to reject the null hypothesis.  When you reject the null hypothesis, this means that there is sufficient evidence to support the alternative hypothesis (H_a).  If the results of the test require you to fail to reject the null hypothesis, this means that there is insufficient evidence to support the alternative hypothesis (H_a). 

The following video provides an overview of the process of hypothesis testing:

The two-sample z-test for proportions is a hypothesis test used to compare the proportions of two independent groups. It’s often used to determine if there is a significant difference between the percentages of individuals in two groups who exhibit a particular characteristic or behavior. The following video provides an overview of the test and tool that can be used to perform the test.