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You can conclude that there is not enough evidence to reject the null hypothesis. Or that your model was incorrectly specified.

Consider the exact equation y = x2. A regression of y against x (for -a < x < a) will give a regression coefficient of 0. Not because there is no relationship between y and x but because the relationship is not linear: the model is wrong! Do a regression of y against x2 and you will get a perfect regression!

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Q: What can you conclude if the global test of regression does not reject the null hypothesis?
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If we reject the null hypothesis what can we conclude about the alpha risk?

If we reject the null hypothesis, we conclude that the alternative hypothesis which is the alpha risk is true. The null hypothesis is used in statistics.


If the decision in the hypothesis test of the population correlation coefficient is to reject the null hypothesis. What can you conclude about the correlation in the population?

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What is the purpose of a conclusion?

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The null hypothesis will not reject - it is a hypothesis and is not capable of rejecting anything. The critical region consists of the values of the test statistic where YOU will reject the null hypothesis in favour of the expressed alternative hypothesis.


When do we reject a hypothesis?

When we've proven that the hypothesis is false !


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Difference between acceptance and rejection region?

Some researchers say that a hypothesis test can have one of two outcomes: you accept the null hypothesis or you reject the null hypothesis. Many statisticians, however, take issue with the notion of "accepting the null hypothesis." Instead, they say: you reject the null hypothesis or you fail to reject the null hypothesis. Why the distinction between "acceptance" and "failure to reject?" Acceptance implies that the null hypothesis is true. Failure to reject implies that the data are not sufficiently persuasive for us to prefer the alternative hypothesis over the null hypothesis.


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Would I accept or reject the null hypothesis if the probability of the obtained statistic is 0.001 and alpha is 0.05?

You should reject the null hypothesis.


Can you accept and reject the null Hypothesis Why or why not?

Some people say you can either accept the null hypothesis or reject it. However, there are statisticians that insist you can either reject it or fail to reject it, but you can't accept it because then you're saying it's true. If you fail to reject it, you're only claiming that the data wasn't strong enough to convince you to choose the alternative hypothesis over the null hypothesis.


What is power function in statistics?

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If the null hypothesis is true and the researchers do not reject it then a correct decision has been made?

True because the point of the hypothesis test is to figure out the probability of the null hypothesis being true or false. If it is tested and it is true, then you do not reject but you reject it, when it is false.