f a hypothesis is rejected at a 5% level of significance, it ___.Group of answer choicesmay be rejected or not rejected at the 1% levelwill always be rejected at the 1% levelwill always be accepted at the 1% levelwill never be tested at the 1% level
Question
f a hypothesis is rejected at a 5% level of significance, it ___.Group of answer choicesmay be rejected or not rejected at the 1% levelwill always be rejected at the 1% levelwill always be accepted at the 1% levelwill never be tested at the 1% level
Solution
If a hypothesis is rejected at a 5% level of significance, it may be rejected or not rejected at the 1% level.
Here's why:
The level of significance, often denoted by alpha (α), is the probability of rejecting the null hypothesis when it is true. In other words, it's the risk of making a Type I error.
When we say a hypothesis is rejected at a 5% level of significance, it means there's a 5% risk of rejecting the null hypothesis when it is true.
However, when we move to a 1% level of significance, we are being more stringent. We are saying we are only willing to accept a 1% risk of rejecting the null hypothesis when it is true.
So, a hypothesis that is rejected at a 5% level may or may not be rejected at a 1% level. It depends on the p-value of the test. If the p-value is less than 1%, then the hypothesis would be rejected at the 1% level. But if the p-value is greater than 1%, then the hypothesis would not be rejected at the 1% level.
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