Conceptual Preparation: Methods of Statistical Inference

Null hypothesis testing

Continuing with the example from the previous lesson, we can use the hypothesis testing method to test whether the unknown population average grade equals some hypothetical value chosen by Joe. Suppose Joe wants to test a null hypothesis that the unknown population mean equals 120. (Joe doesn’t know the true population average grade is 150, but feeling challenged, he wonders whether it could be very low at 120 or D). Based on certain assumptions, Joe can construct a test statistic such as a Z- or t-statistic (depending on sample size and whether the population standard deviation is known). This test statistic measures the weighted distance between the sample estimate and the hypothetical population parameter based on certain assumptions.