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When is rejected at , it implies that . Changing the level of significance to would not necessarily lead to rejection of since .
When is rejected at , it implies that . Changing the level of significance to would lead to rejection of also since .
Let be the p-value for an upper tailed test and be the p-value of a two tailed test.
When is rejected at a given for an upper tailed test it shows that .
The relationship between the p-value for these tests is,
Clearly, the p-value of a two tailed test will be large since the upper tailed p-value was small. Thus, the null hypothesis would not be rejected.