The Odds of Finding Significance For a two-tailed test of a hypothesis, each of the critical regions would be bounded by ___ if you chose
A).01
B).025
C).05
D).10

Question

Quizplus · Accepted Answer

For a two-tailed test with a significance level of α = .01, the critical regions would be divided equally between the two tails, meaning that each tail would have an area of .01/2 = .005. To determine the boundaries of each tail, we would look up the z-score corresponding to .005 in the standard normal distribution table, which is approximately ±2.58. Therefore, the critical values for this test would be -2.58 and +2.58, and any test statistic falling outside of these bounds would be considered statistically significant at the α = .01 level.

The same logic applies for a significance level of α = .025, which is the midpoint between α = .01 and α = .05. In this case, each tail would have an area of .025/2 = .0125, and the critical values would be -1.96 and +1.96.

Choosing a significance level of α = .05 or α = .10 would result in larger critical regions and less strict criteria for statistical significance. For example, with α = .05, each tail would have an area of .05/2 = .025, and the critical values would be -1.64 and +1.64.

The Odds of Finding Significance for a Two-Tailed Test of a Hypothesis