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Our teacher told us

If a test is rejected at 1% level of significance , then it will be rejected at 5% , 10% level of significance .

I don't understand how does the rejection at 1% level of significance imply rejection at 5% , 10% level of significance ?

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Not completely correct. A better statement is that a test that rejects at 1% will have been rejected at 5%, 10%, etc. You shouldn't change the threshold for a test once it is set prior to the experiment.

The threshold at significance level x% is set such that x% of the distribution (by area under the density curve) lies beyond the threshold. Rejection means that the statistic you are checking against the distribution falls in this area. So if it falls in the 1% area, it will have also fallen in the 5% area, etc.

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    $\begingroup$ If you are going to use the future perfect then perhaps you should move it out of the indicative, e.g. to "would have been rejected". You may also need to say the the "1%" represents the probability of erroneously rejecting the null hypothesis when it is in fact true, so "5%" involves that possibility and more. $\endgroup$ – Henry Jul 3 '15 at 16:24
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    $\begingroup$ The phrase "beyond the threshold" suggests you have in mind a particular kind of hypothesis test which is not universally applicable. To be more general you should consider referring to "critical regions" rather than any particular threshold. The reference to a "density curve" also presupposes a narrow application. Many test statistics--especially those involved in non-parametric procedures--have no density at all. $\endgroup$ – whuber Jul 3 '15 at 16:46

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