SOLUTION: Help pleaseee - Consider a test for mue(mean). A) if the p-value is such that you can reject H_0 at the 1% level signifucance, can you always reject H

SOLUTION: Help pleaseee - Consider a test for mue(mean). A) if the p-value is such that you can reject H_0 at the 1% level signifucance, can you always reject H_0 at 5% level significance

Question 930136: Help pleaseee
- Consider a test for mue(mean).
A) if the p-value is such that you can reject H_0 at the 1% level signifucance, can you always reject H_0 at 5% level significance? Explain why or why not.
B) 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? Explain why or why not.
I have to show all the work!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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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