Accept/Reject Null Hypothesis Using Confidence Intervals

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To accept or reject a null hypothesis using confidence intervals, one must compare the interval range to a specific value. If the value lies outside the confidence interval, the null hypothesis can be rejected, while if it lies within, the null hypothesis is accepted. Confidence levels are directly related to significance levels, meaning a confidence interval cannot be interpreted in isolation from its significance level. Therefore, it is incorrect to accept or reject a null hypothesis solely based on a confidence interval without considering the associated significance level. Understanding this relationship is crucial for accurate statistical analysis.
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Hello. I am teaching myself statistics and my question is about confidence intervals. I understand that I can accept or reject a null hypothesis based on comparing my p values to the significance value (say .05)
But how do i accept or reject a null hypothesis based SOLELY on
a given confidence intervals say -12 to 1.4?
thanks

blumfeld0
 
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Say you have a confidence interval of 99% confidence, and the range is (-12, 1.4). If you have a number that lies outside of that range (let's say 1.9), then you can reject H_0 (and accept H_a) at \alpha = .01. If the number does lie inside that range (let's say -3), then you accept H_0 (and reject H_a).
 
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Hi. Thanks for your reply. That is the problem. A colleaugue of mine told me that you can accept or reject the null hypothesis solely given the confidence interval without being given the actual data or significance level (99%, 95%)
Is he right?
if so how?
thanks

blumfeld0
 
a confidence level always has a significance level associated with it, so no.
 
Confidence level = 1 - significance level
 
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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