Null Hypotheses And Alternate Hypotheses Hypothesis Testing Hypotheses

Null Hypotheses And Alternate Hypotheses

Hypothesis Testing Hypotheses are always about the population and never about the sample. The true value of a hypothesis can never be known or confirmed. Conclusions regarding hypotheses are never absolute and as such are susceptible to some degree of definable/calculable risk of error. Type I Error Type II Error Rejecting H 0 when H 0 is True Failing to Reject H 0 when H 0 is False Probability of Type I Error = α Probability of Type II Error = β

Power of the Test Probability of Correctly Rejecting a False Null Hypothesis = 1 - β Probability of Correctly Rejecting H 0 when H 1 is true = 1 - β Probability of Rejecting H 0 when H 0 is False = 1 - β Probability of Accepting H 1 when H 1 is True = 1 - β

Probability of Type I and Type II Errors The Level of Significance α establishes the Probability of a Type I Error. The Probability of a Type II Error depends on the magnitude of the true mean and the sample size.

Probability of Type II Errors Consider H 0: μ = μ 0 H 1: μ ≠ μ 0 Suppose the null hypothesis is false and the true magnitude of the mean is μ = μ 0 + δ. and therefore , that is to say Z 0 is normally distributed with mean and variance 1.

Probability of Type II Error Applied Statistics and Probability for Engineers, 3 ed, Montgomery & Runger, Wiley 2003