Question 930136
Rule: if the p-value is less than alpha, then you reject the null hypothesis H0. The same is true in reverse. If we rejected H0, then the p-value is less than alpha.


alpha = level of significance


A)

"if the p-value is such that you can reject H_0 at the 1% level significance"


Given that quote above, we know for a fact that the p-value is less than 0.01. So the p-value is certainly also less than 0.05


Question: "can you always reject H_0 at 5% level significance?"


Answer: Yes we always can because whatever the p-value is, it's certainly less than 0.05 (since it's less than 0.01 already)


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B)


Now we flip part A) around. If we know the p-value is less than 0.05, then it's not always going to be less than 0.01 at the same time. The p-value could be 0.02


0.02 is certainly less than 0.05 but it's NOT less than 0.01


Question: "if the p-value is such that you can reject H_0 at the 5% level of significance, can you always reject H_0 at the 1% level significance?"


Answer: No we cannot always reject H0 at the 1% significance level (see explanation above)

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