A question about hypothesis testing

[Artusartos]

The significance level of a test is the probability that the null hypothesis is rejected when it is true, right? And the critical region is the region that we reject the null hypothesis...so can the significance level be calculated by finding the probability of being in the critical region?

Thanks in advance

 

[Simon Bridge]

the critical region is the region that we reject the null hypothesis

The critical region of a hypothesis test is the set of all outcomes which cause the null hypothesis to be rejected in favor of the alternative hypothesis.
http://en.wikipedia.org/wiki/Statistical_hypothesis_testing

The significance level of a test is the probability that the null hypothesis is rejected when it is true, right?

The significance level is usually denoted by the Greek symbol α (lowercase alpha). Popular levels of significance are 10% (0.1), 5% (0.05), 1% (0.01), 0.5% (0.005), and 0.1% (0.001). If a test of significance gives a p-value lower than the significance level α, the null hypothesis is rejected. Such results are informally referred to as 'statistically significant'. For example, if someone argues that "there's only one chance in a thousand this could have happened by coincidence", a 0.001 level of statistical significance is being implied. The lower the significance level chosen, the stronger the evidence required. The choice of significance level is somewhat arbitrary, but for many applications, a level of 5% is chosen by convention.
http://en.wikipedia.org/wiki/Significance_level

can the significance level be calculated by finding the probability of being in the critical region?

Wouldn't you normally do it the other way around?
How would you choose the critical region?

 

[Artusartos]

The critical region of a hypothesis test is the set of all outcomes which cause the null hypothesis to be rejected in favor of the alternative hypothesis.
http://en.wikipedia.org/wiki/Statistical_hypothesis_testing The significance level is usually denoted by the Greek symbol α (lowercase alpha). Popular levels of significance are 10% (0.1), 5% (0.05), 1% (0.01), 0.5% (0.005), and 0.1% (0.001). If a test of significance gives a p-value lower than the significance level α, the null hypothesis is rejected. Such results are informally referred to as 'statistically significant'. For example, if someone argues that "there's only one chance in a thousand this could have happened by coincidence", a 0.001 level of statistical significance is being implied. The lower the significance level chosen, the stronger the evidence required. The choice of significance level is somewhat arbitrary, but for many applications, a level of 5% is chosen by convention.
http://en.wikipedia.org/wiki/Significance_levelWouldn't you normally do it the other way around?
How would you choose the critical region?

No they gave me the critical region and I have to find the significance level...so I just calculate it from the critical region, right?

 

[Simon Bridge]

Yeah - without seeing the problem in question, I would just reverse the usual procedure.