MHB True or false questions involving the null hypothesis

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The null hypothesis is assumed true until evidence suggests otherwise. A P-value greater than the significance level leads to failing to reject the null hypothesis, not confirming it as true. Rejecting the null hypothesis does not mean the alternative hypothesis is accepted; it simply indicates the null is rejected. Both hypotheses cannot be rejected simultaneously at a significance level. A P-value less than the significance level results in rejecting the null hypothesis.
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1) The null hypothesis represents the condition that will be assumed to be true unless sufficient
evidence is presented to show that the condition has changed.

True.

2) A P-value greater than the chosen level of significance results in concluding the null hypothesis is
true.

True.

3) The alternative hypothesis will be accepted to be true if the null hypothesis is rejected.

True.

4) Sometimes both the null and alternative hypotheses can be rejected at a level of
significance.

False.

5) A P-value less than the chosen level of significance results in rejecting the null hypothesis.

True.

Am I right or wrong?
 
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Re: True or false

Uniman said:
1) The null hypothesis represents the condition that will be assumed to be true unless sufficient
evidence is presented to show that the condition has changed.

True.



Correct
Uniman said:
2) A P-value greater than the chosen level of significance results in concluding the null hypothesis is
true.

True.



Yes, but we say "we fail to reject the null hypothesis", we don't say the null hypothesis is true
Uniman said:
3) The alternative hypothesis will be accepted to be true if the null hypothesis is rejected.

True.



No, we don't accept the alternate hypothesis, we reject the null hypothesis. It's all in the words we use.

Uniman said:
4) Sometimes both the null and alternative hypotheses can be rejected at a level of
significance.

False.



correct

Uniman said:
5) A P-value less than the chosen level of significance results in rejecting the null hypothesis.

True.
Uniman said:



correct
 
The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...

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