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If 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

If 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

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Solution

The correct answer is "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 likelihood of making a Type I error.

If a hypothesis is rejected at a 5% level of significance, it means there's a 5% chance of incorrectly rejecting the null hypothesis.

However, when we move to a 1% level of significance, we're being more stringent. We're saying we'll only reject the null hypothesis if there's a 1% or less chance of being wrong.

So, a hypothesis that's rejected at a 5% level may or may not be rejected at a 1% level. It depends on the specific p-value of the hypothesis test. If the p-value is less than or equal to 1%, then the hypothesis would be rejected at the 1% level. But if the p-value is greater than 1%, the hypothesis would not be rejected at the 1% level.

This problem has been solved

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