Q: What is the definition of a statistical null hypothesis?

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Power analysis can be used to calculate statistical significance. It compares the null hypothesis with the alternative hypothesis and looks for evidence that can reject the null hypothesis.

It is the hypothesis that is presumed true until statistical evidence in the form of a hypothesis test proves it is not true.

No. The null hypothesis is not considered correct. It is an assumption, and hypothesis testing is a consistent meand of determining whether the data is sufficiently strong to say that it may be untrue. The data either supports the alternative hypothesis or it fails to reject it. See examples in links. Also note this quote from Wikipedia: "Statistical hypothesis testing is used to make a decision about whether the data contradicts the null hypothesis: this is called significance testing. A null hypothesis is never proven by such methods, as the absence of evidence against the null hypothesis does not establish it."

The null hypothesis is an hypothesis about some population parameter. The goal of hypothesis testing is to check the viability of the null hypothesis in the light of experimental data. Based on the data, the null hypothesis either will or will not be rejected as a viable possibility.

Be able to reject the null hypothesis and accept the research hypothesis

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Power analysis can be used to calculate statistical significance. It compares the null hypothesis with the alternative hypothesis and looks for evidence that can reject the null hypothesis.

The z-score is a statistical test of significance to help you determine if you should accept or reject the null-hypothesis; whereas the p-value gives you the probability that you were wrong to reject the null-hypothesis. (The null-hypothesis proposes that NO statistical significance exists in a set of observations).

It is the hypothesis that is presumed true until statistical evidence in the form of a hypothesis test proves it is not true.

It is the hypothesis that is presumed true until statistical evidence in the form of a hypothesis test proves it is not true.

with the alternative hypothesis the reasearcher is predicting

In fact, any statistical relationship in a sample can be interpreted in two ways: ... The purpose of null hypothesis testing is simply to help researchers decide ... the null hypothesis in favour of the alternative hypothesisâ€”concluding that there is a ...

No, that is not the correct definition.

The null hypothesis is typically tested using statistical tests such as t-tests, ANOVA, or chi-square tests. These tests calculate the probability of obtaining the observed data if the null hypothesis were true. If this probability (p-value) is below a certain threshold (usually 0.05), the null hypothesis is rejected.

The power of a statistical test is the probability that the test will reject the null hypothesis when it is, in fact, false. Please see the link.

The observed value is unlikely to have occured purely bt chance under the null hypothesis and, as a consequence, you ought to reject the null in favour of the alternative hypothesis.

Statistical tests are designed to test one hypothesis against another. Conventionally, the default hypothesis is that the results were obtained purely by chance and that there is no observed effect acting on the observations - ie the effect is null. The alternative is that there IS an effect.

Because the statistical test will compare the probability of the outcome under the null hypothesis in relation to the outcome under either a dierectional or non-directional alternative hypothesis.