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A statistical significance test starts with a random sample from a population. If the sample data are consistent with the null hypothesis, then you do not reject the null hypothesis; if the sample data are inconsistent with the null hypothesis, then you reject the null hypothesis and conclude that the alternative hypothesis is true. [3]
Let p = Pr(X > Y), and then test the null hypothesis H 0: p = 0.50. In other words, the null hypothesis states that given a random pair of measurements (x i, y i), then x i and y i are equally likely to be larger than the other. To test the null hypothesis, independent pairs of sample data are collected from the populations {(x 1, y 1), (x 2, y ...
This is why the hypothesis under test is often called the null hypothesis (most likely, coined by Fisher (1935, p. 19)), because it is this hypothesis that is to be either nullified or not nullified by the test. When the null hypothesis is nullified, it is possible to conclude that data support the "alternative hypothesis" (which is the ...
An example of Neyman–Pearson hypothesis testing (or null hypothesis statistical significance testing) can be made by a change to the radioactive suitcase example. If the "suitcase" is actually a shielded container for the transportation of radioactive material, then a test might be used to select among three hypotheses: no radioactive source ...
How to perform a Z test when T is a statistic that is approximately normally distributed under the null hypothesis is as follows: First, estimate the expected value μ of T under the null hypothesis, and obtain an estimate s of the standard deviation of T. Second, determine the properties of T : one tailed or two tailed.
In statistical hypothesis testing, two hypotheses are compared. These are called the null hypothesis and the alternative hypothesis. The null hypothesis is the hypothesis that states that there is no relation between the phenomena whose relation is under investigation, or at least not of the form given by the alternative hypothesis.
An example can be whether a machine produces more than one-percent defective products. In this situation, if the estimated value exists in one of the one-sided critical areas, depending on the direction of interest (greater than or less than), the alternative hypothesis is accepted over the null hypothesis.
Thus, the null hypothesis is rejected if >, (where , is the upper tail critical value for the distribution). Bartlett's test is a modification of the corresponding likelihood ratio test designed to make the approximation to the χ k − 1 2 {\displaystyle \chi _{k-1}^{2}} distribution better (Bartlett, 1937).