Sample of n = 16 values from normal population with σ = 4

H0 :   μ = 10
HA :   μ > 10

Decision
  accept H0     reject H0  
Truth H0 is true     
HA (H0 is false)      

 

Use this diagram to:

The diagram is for a 1-tailed test for µ based on known σ. Drag the top slider to move the cut-off for accepting/rejecting H0 and see why it is impossible to simultaneously decrease both error probabilities.

There is a trade-off between the acceptable sizes of the two types of error.

Adjust the cut-off to make prob(Type I error) = 0.05. Say that this is the decision rule for a 5% significance level. Adjust the cut-off for a decision rule with 1% significance level.

For a test with 5% significance level, k = 11.64.

Mention that the alternative hypothesis includes many different values of µ. Drag the slider at the bottom left to alter µ and note that the probability of a Type II error changes. However changing the cut-off at the top still involves this trade-off between the two types of error.