Suppose that some hypothesis H_0 was rejected at the α1 = 0.05 level of significance. If the same hypothesis test is repeated with the same evidence but at the new significance level of α2 = 0.01 then which of the following are true? Select one or more answers.Group of answer choicesH_0 may be retained.The p-value of the second test will be higher.H_0 will be rejected.The p-value of the second test will be lower.H_0 will be retained.
Question
Suppose that some hypothesis H_0 was rejected at the α1 = 0.05 level of significance. If the same hypothesis test is repeated with the same evidence but at the new significance level of α2 = 0.01 then which of the following are true? Select one or more answers.Group of answer choicesH_0 may be retained.The p-value of the second test will be higher.H_0 will be rejected.The p-value of the second test will be lower.H_0 will be retained.
Solution
The correct answer is "H_0 may be retained."
Here's why:
The level of significance (α) is the probability of rejecting the null hypothesis (H_0) when it is true. A lower α means a lower chance of rejecting H_0, making the test more conservative.
So, if a hypothesis is rejected at α1 = 0.05, it might not be rejected at a lower significance level of α2 = 0.01 because the evidence might not be strong enough to reject the null hypothesis at this lower level.
The p-value is the smallest level of significance at which we would still reject the null hypothesis. It does not change with the level of significance. So, the p-value of the second test will not be higher or lower, it will be the same as in the first test.
Therefore, the statement "H_0 may be retained" is true. The other statements are not necessarily true.
Similar Questions
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