1 it prevents us from looking at the data and then

Info icon This preview shows pages 64–74. Sign up to view the full content.

View Full Document Right Arrow Icon
1. It prevents us from looking at the data and then deciding on the relevant alternative. 2. It is harder to reject a null against a two-sided alternative, forcing us to find even stronger evidence against H 0 before we reject it. 64
Image of page 64

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
We use the same test statistic, T X ̄ 0 / n n X ̄ 0 , but our rejection rule changes. We want to have power against 0 and 0 . We use a symmetric rule: Reject H 0 in favor of H 1 if | T | c for a suitable critical value c 0. Equivalently, reject H 0 if T c or T c . 65
Image of page 65
As before, the choice of c is based based on the size of the test. If, for example, .05, we need to find the value c such that P | Z | c .05 where Z Normal 0,1 . Equivalently, P | Z | c .95 or P c Z c .95 or c c .95 66
Image of page 66

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Now use the symmetry of the standard normal distribution: c 1 c . Plug in and solve to get c .975 or c 1 .975 1.96 67
Image of page 67
For a two-sided alternative, the critical value for a size 5% test is now the 97.5 percentile in a standard normal distribution. The rejection rule, at the 5% size, is | T | 1.96 Compared with a one-sided alternative, we require a larger statistic in absolute value before we reject the null hypothesis: 1.96 compared with 1.65 (for H 1 : 0 ). A test against a two-sided alternative is called a two - tailed test . 68
Image of page 68

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon