Decision Theory
Null Hypotheses
H0 - no difference, zero effect
Alternative hypotheses
H1 - hypothesis that differs from H0

Significance level test [1]
The way to reject the null hypothesis, based on the significant evidence against the hypothesis.
In practice, a significance level of 0.05 or 0.01 are chosen. For example, α=0.05 means that we are 95% confident that we have made the right decision.
Reject the hypothesis if the normalized z score lies outside the critical interval in the following table:

Level of significance, α 0.1 0.05 0.01 0.005
Critical interval, one-tailed z<1.28 z<1.645 z<2.33 z<2.58
Critical interval, two-tailed |z|<1.645 |z|<1.96 |z|<2.58 |z|<2.81

Accept the hypothesis otherwise (or, if desired, make no decision at all).

1. M.R. Spiegel, D.P. Lindstrom, "Schaum's Easy Outline: Statistics," McGraw-Hill, 1999.
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