Select all correct statement(s). Note that incorrectly-selected statements will draw penalty. Group of answer choices We know the probability of making a Type I error given that the null is true. The null hypothesis is rejected if the p-value is lower than the level of significance. For an upper-tail test, the 1% critical value must be greater than the 5% critical value. We know the probability of making a Type II error if the null is known to be false. Once the null hypothesis is rejected at 1%, it is unnecessary to test at 5%. When other factors remain the same, the lower the level of significance the lower the power. The critical value method and the p-value method can lead to a different conclusions from each other. The lower the power the lower the probability of Type II error.

The correct statements are:

1. We know the probability of making a Type I error given that the null is true.
2. The null hypothesis is rejected if the p-value is lower than the level of significance.
3. For an upper-tail test, the 1% critical value must be greater than the 5% critical value.
4. Once the null hypothesis is rejected at 1%, it is unnecessary to test at 5%.
5. When other factors remain the same, the lower the level of significance the lower the power.

The incorrect statements are:

1. We know the probability of making a Type II error if the null is known to be false. (This is incorrect because the probability of making a Type II error is not known, it depends on the true value of the parameter being tested)
2. The critical value method and the p-value method can lead to a different conclusions from each other. (This is incorrect because both methods should lead to the same conclusion)
3. The lower the power the lower the probability of Type II error. (This is incorrect because the power of a test is the probability that it correctly rejects a false null hypothesis. Therefore, the lower the power, the higher the probability of a Type II error)