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When the null hypothesis is true the t statistic will have an average value of?
Wiki User
∙ 11y ago
"Whenever the t-statistic is farther from 0 than the t-critical value, the null hypothesis is rejected; otherwise, the null hypothesis is retained"
Example: t = (M-μ0)/ (SD / Sqrt N)
M is the sample mean and μ0 is the hypothetical mean. For a paired-samples t-test, M is the mean of the difference scores and μ0 is 0. SD is the standard deviation (of the difference scores in the case of a paired-samples t-test) and N is the number of subjects in the sample.
Wiki User
∙ 11y ago
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What is the difference between a test statistic and a critical value?
A test statistic is a value calculated from a set of observations. A critical value depends on a null hypothesis about the distribution of the variable and the degree of certainty required from the test. Given a null hypothesis it may be possible to calculate the distribution of the test statistic. Then, given an alternative hypothesis, it is may be possible to calculate the probability of the test statistic taking the observed (or more extreme) value under the null hypothesis and the alternative. Finally, you need the degree of certainty required from the test and this will determine the value such that if the test statistic is more extreme than the critical value, it is unlikely that the observations are consistent with the hypothesis so it must be rejected in favour of the alternative hypothesis. It may not always be possible to calculate the distribution function for the variable.
What values are specified by the null hypothesis for the chi square test for goodness or fit?
The value specified is usually the maximum value that the test statistic can take for a given level of statistical significance when the null hypothesis is true. This value will depend on the parameter of the chi-square distribution which is also known as its degrees of freedom.The value specified is usually the maximum value that the test statistic can take for a given level of statistical significance when the null hypothesis is true. This value will depend on the parameter of the chi-square distribution which is also known as its degrees of freedom.The value specified is usually the maximum value that the test statistic can take for a given level of statistical significance when the null hypothesis is true. This value will depend on the parameter of the chi-square distribution which is also known as its degrees of freedom.The value specified is usually the maximum value that the test statistic can take for a given level of statistical significance when the null hypothesis is true. This value will depend on the parameter of the chi-square distribution which is also known as its degrees of freedom.
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.
When you reject the Null Hypothesis that means that the Null Hypothesis cannot be correct?
No. Rejecting the Null Hypothesis means that there is a high degree of probability that it is not correct. This degree of probability is the critical level that you choose for the test statistic. However, there is still a small probability that the null hypothesis was correct.
What is the conclusion if the test statistic is the same as the critical value?
Any decision based on the test statistic is marginal in such a case. It is important to remember that the test statistic is derived on the basis of the null hypothesis and does not make use of the distribution under the alternative hypothesis.
What value does the null hypothesis make a claim about?
sample statistic
What is the meaning of null hypthesis being rejected?
You may want to prove that a given statistic of a population has a given value. This is the null hypothesis. For this you take a sample from the population and measure the statistic of the sample. If the result has a small probability of being (say p = .025) if the null hypothesis is correct, then the null hypothesis is rejected (for p = .025) in favor of an alternative hypothesis. This can be simply that the null hypothesis is incorrect.
What does the critical value represent?
The critical value is used to test a null hypothesis against an alternative hypothesis at some pre-defined level of significance. A test statistic is calculated from the outcomes of a set of trials and if this test statistic is more extreme than the critical value then the null hypothesis must be rejected in favour of the alternative.
What causes hypothesis to be rejected?
We have two types of hypothesis i.e., Null Hypothesis and Alternative Hypothesis. we take null hypothesis as the same statement given in the problem. Alternative hypothesis is the statement that is complementary to null hypothesis. When our calculated value is less than the tabulated value, we accept null hypothesis otherwise we reject null hypothesis.
What does a p value of 0.66 tell us?
A p-value is the probability of obtaining a test statistic as extreme or more extreme than the one actually obtained if the null hypothesis were true. If this p-value is less than the level of significance (usually set by the experimenter as .05 or .01), we reject the null hypothesis. Otherwise, we retain the null hypothesis. Therefore, a p-value of 0.66 tell us not to reject the null hypothesis.
What is the difference between a test statistic and a critical value?
A test statistic is a value calculated from a set of observations. A critical value depends on a null hypothesis about the distribution of the variable and the degree of certainty required from the test. Given a null hypothesis it may be possible to calculate the distribution of the test statistic. Then, given an alternative hypothesis, it is may be possible to calculate the probability of the test statistic taking the observed (or more extreme) value under the null hypothesis and the alternative. Finally, you need the degree of certainty required from the test and this will determine the value such that if the test statistic is more extreme than the critical value, it is unlikely that the observations are consistent with the hypothesis so it must be rejected in favour of the alternative hypothesis. It may not always be possible to calculate the distribution function for the variable.
How do you perform a Statistical Hypothesis Testing?
To start with you select your hypothesis and its opposite: the null and alternative hypotheses. You select a confidence level (alpha %), which is the probability that your testing procedure rejects the null hypothesis when, if fact, it is true.Next you select a test statistic and calculate its probability distribution under the two hypotheses. You then find the possible values of the test statistic which, if the null hypothesis were true, would only occur alpha % of the times. This is called the critical region.Carry out the trial and collect data. Calculate the value of the test statistic. If it lies in the critical region then you reject the null hypothesis and go with the alternative hypothesis. If the test statistic does not lie in the critical region then you have no evidence to reject the null hypothesis.
What is test statistic?
This is used in statistic to know whether to accept or reject a null hypothesis or alternative hypothesis
What values are specified by the null hypothesis for the chi square test for goodness or fit?
The value specified is usually the maximum value that the test statistic can take for a given level of statistical significance when the null hypothesis is true. This value will depend on the parameter of the chi-square distribution which is also known as its degrees of freedom.The value specified is usually the maximum value that the test statistic can take for a given level of statistical significance when the null hypothesis is true. This value will depend on the parameter of the chi-square distribution which is also known as its degrees of freedom.The value specified is usually the maximum value that the test statistic can take for a given level of statistical significance when the null hypothesis is true. This value will depend on the parameter of the chi-square distribution which is also known as its degrees of freedom.The value specified is usually the maximum value that the test statistic can take for a given level of statistical significance when the null hypothesis is true. This value will depend on the parameter of the chi-square distribution which is also known as its degrees of freedom.
Can you accept a null hypothesis under the t statistic and then reject the same null hypothesis using the F statistic?
At the same level of significance and against the same alternative hypothesis, the two tests are equivalent.
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.
What is the reason of a null hypothesis being rejected?
W The test statistic is is the critical region or it exceeds the critical level. What this means is that there is a very low probability (less than the critical level) that the test statistics could have attained a value as extreme (or more extreme) if the null hypothesis were true. In simpler terms, if the null hypothesis were true you are very, very unlikely to get such an extreme value for the test statistic. And although it is possible that this happened purely by chance, it is more likely that the null hypothesis was wrong and so you reject it.
