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A statistician may have some idea about some statistics in a data set, and there is a need to test whether or not that hypothesis is likely to be true. Data are collected and a test statistic is calculated. The value of this test statistic is used to determine the probability that the hypothesis is true.
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What is the basic requirement of a scientific hypothesis?
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What is test statistic. Why do you have to know the distribution of a test statistic?
A test statistic is used to test whether a hypothesis that you have about the underlying distribution of your data is correct or not. The test statistic could be the mean, the variance, the maximum or anything else derived from the observed data. When you know the distribution of the test statistic (under the hypothesis that you want to test) you can find out how probable it was that your test statistic had the value it did have. If this probability is very small, then you reject the hypothesis. The test statistic should be chosen so that under one hypothesis it has one outcome and under the is a summary measure based on the data. It could be the mean, the maximum, the variance or any other statistic. You use a test statistic when you are testing between two hypothesis and the test statistic is one You might think of the test statistic as a single number that summarizes the sample data. Some common test statistics are z-score and t-scores.
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.
When can a null hypothesis be rejected?
Usually when the test statistic is in the critical region.
How is the critical region utilized in hypothesis testing?
When you formulate and test a statistical hypothesis, you compute a test statistic (a numerical value using a formula depending on the test). If the test statistic falls in the critical region, it leads us to reject our hypothesis. If it does not fall in the critical region, we do not reject our hypothesis. The critical region is a numerical interval.
