We conducted a hypothesis test for a population parameter at alpha = 0.01 and we failed to rejected Ho.
If we decided to use alpha = 0.05, how would our conclusion change?
A) At alpha = 0.05, we would still fail to reject HO.
B) At alpha = 0.05, we would reject HO.
C) It is not possible to answer without knowing the actual p-value from the hypothesis test.
Answer A?
C. Is the .05 > Alpha > .01? We don’t know.
Excuse me. Is .05 > P > .01? Again, we don’t know.
The correct answer is C) It is not possible to answer without knowing the actual p-value from the hypothesis test.
When conducting a hypothesis test, the decision to reject or fail to reject the null hypothesis (Ho) is based on comparing the p-value, which is the probability of observing a test statistic as extreme as the one observed or more extreme, assuming Ho is true, with the chosen significance level (alpha).
In this case, you mentioned that at alpha = 0.01, the decision was to fail to reject Ho. However, without knowing the actual p-value obtained from the hypothesis test, we cannot determine whether or not the conclusion would change if alpha is changed to 0.05.
If the p-value is less than 0.05, then changing alpha from 0.01 to 0.05 would not change the conclusion, and we would still fail to reject Ho. However, if the p-value is between 0.01 and 0.05, then changing alpha to 0.05 might lead to rejecting Ho.
Therefore, we need the actual p-value to determine the impact of changing the significance level on the conclusion of the hypothesis test.