Page 546 - Probability and Statistical Inference

11. Likehood Ratio and Other Tests 523

to a one-sample problem in terms of the pivot

Under the null hypothesis H : µ = µ , the statistic U has the Student’s t
2
1
0
distribution with n – 1 degrees of freedom.
Upper-Sided Alternative Hypothesis
We test H : µ = µ versus H : µ > µ . See the Figure 11.4.1. Along the
2
2
1
1
1
0
lines of Section 8.4, we can propose the following upper-sided level α test:

Figure 11.4.1. Upper-Sided Student’s t Rejection Region
n-1
Lower-Sided Alternative Hypothesis
We test H : µ = µ versus H : µ < µ . See the Figure 11.4.2. Along the
1
2
1
0
1
2
lines of Section 8.4, we can propose the following lower-sided level α test:

Figure 11.4.2. Lower-Sided Student’s t Rejection Region
n-1