If the null hypothesis is rejected at the .01 alpha level, it will be rejected at the .05 alpha level.
Is this correct?
Null hypothesis will be rejected if p ≤ .01.
Is .05 < .01?
No, that statement is not correct.
To understand why, let's first explain what the null hypothesis and alpha level are in hypothesis testing.
In hypothesis testing, the null hypothesis (H0) is a statement that suggests there is no significant difference or relationship between variables. On the other hand, the alternative hypothesis (HA) suggests that there is a significant difference or relationship between the variables.
The alpha level (α) represents the significance level, also known as the probability of making a Type I error. It is the predetermined threshold that researchers use to determine whether there is enough evidence to reject the null hypothesis.
Now, let's address the statement itself. If the null hypothesis is rejected at the 0.01 alpha level, it means that the observed data is considered statistically significant at a very strict significance level. In other words, the evidence against the null hypothesis is strong at this level of significance.
However, when we consider the 0.05 alpha level, it is a less strict criterion for rejecting the null hypothesis. If the null hypothesis is already rejected at the 0.01 alpha level, it doesn't necessarily mean that it will be rejected at the 0.05 alpha level.
In fact, if the null hypothesis is rejected at the 0.01 alpha level, it indicates that the evidence is even stronger than what is required at the 0.05 alpha level. Thus, if the null hypothesis is rejected at a more stringent alpha level, it would also be rejected at a less stringent alpha level.
In conclusion, if the null hypothesis is rejected at the 0.01 alpha level, it does not guarantee that it will be rejected at the 0.05 alpha level.