Consider the following random sample. Each experimental unit in the sample was measured twice: once before a treatment (Xi), and once after a treatment (Yi). Is there evidence of a positive mean difference as a result of the treatment? Use a 5% level of significance.
| Xi | 6.3 | 5.8 | 8.6 | 9.4 | 9.7 | 10.1 | 13.1 | 9.1 |
|---|---|---|---|---|---|---|---|---|
| Yi | 7.1 | 5.6 | 8.8 | 9 | 10.4 | 10.5 | 13.7 | 9.6 |
a) Write out the null and alternate hypothesis.
b) Carry out the procedure ("crunch the numbers"):
Standardized test statistic:
P-value:
c) Write a conclusion in context.