General Formula for Testing Hypotheses (1 of 3)

The formula shown below is used for testing hypotheses about a parameter.

The "statistic" is an estimate of the parameter in question. The "hypothesized value" is the value of the parameter specified in the null hypothesis. The standard error of the statistic is assumed to be known and the sampling distribution of the statistic is assumed to normal.

Consider an experiment designed to test the null hypothesis that µ = 10. The test would be conducted with the following formula:

where M (the statistic) is the sample mean, 10 is the hypothesized value of µ, and σM is standard error of the mean. Once z is determined, the probability value can be found using a z table. For example, if M = 15 and σM = 2, then z would be (15-10)/2 = 2.5. The two-tailed probability value would be 0.0124. The one-tailed probability value would be 0.0124/2 = 0.0062.