Using the P–value

1. One–tailed test ( H_a: d > d₀ OR H_a: d < d₀, where d is the parameter of interest):
   1. if P–value ≤ α, then reject H₀ at the α significance level
   2. if P–value > α, then fail to reject H₀ at the α significance level
      
      
2. Two–tailed test ( H_a: d ≠ d₀, where d is the parameter of interest):
   1. if P–value ≤ α/2, then reject H₀ at the α significance level
   2. if P–value > α/2, then fail to reject H₀ at the α significance level

Using C–Level Confidence Intervals

1. One–tailed test ( H_a: d > d₀ OR H_a: d < d₀, where d is the parameter of interest):
   1. cannot use confidence intervals...
      
      
2. Two–tailed test ( H_a: d ≠ d₀, where d is the parameter of interest):
   1. if d is NOT contained in the CI, then reject H₀ at C confidence level
   2. if d is contained in the CI, then fail to reject H₀ at C confidence level

Using the Test Statistic

Finding the Critical Value

First, find the critical value for a given α significance level. For example, to find the critical value, Z_c, for the z–test on the TI83:

1. One–tailed test using α significance level:
   1. for H_a: d < d₀, use invNorm(α, μ, σ)
   2. for H_a: d > d₀, use invNorm(1 – α, μ, σ)
      
      
2. Two–tailed test using α significance level:
   1. use invNorm(α/2, μ, σ)

Making the Conclusion

1. One–tailed test using α significance level:
   1. for H_a: d < d₀, if Z–statistic ≤ Z_c, then reject H₀
   2. for H_a: d > d₀, if Z–statistic ≥ Z_c, then reject H₀
   3. otherwise, fail to reject H₀
      
      
2. Two–tailed test using α significance level:
   1. if | Z–statistic | ≥ Z_c, then reject H₀
   2. if | Z–statistic | < Z_c, then fail to reject H₀