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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] Consider the following example.
The null hypothesis is that the subject has no ability to distinguish the teas. In Fisher's approach, there was no alternative hypothesis, [2] unlike in the Neyman–Pearson approach. The test statistic is a simple count of the number of successful attempts to select the four cups prepared by a given method.
For example, if one test is performed at the 5% level and the corresponding null hypothesis is true, there is only a 5% risk of incorrectly rejecting the null hypothesis. However, if 100 tests are each conducted at the 5% level and all corresponding null hypotheses are true, the expected number of incorrect rejections (also known as false ...
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 ...
The sign test is a statistical test for consistent differences between pairs of observations, such as the weight of subjects before and after treatment. Given pairs of observations (such as weight pre- and post-treatment) for each subject, the sign test determines if one member of the pair (such as pre-treatment) tends to be greater than (or less than) the other member of the pair (such as ...
In statistics, an F-test of equality of variances is a test for the null hypothesis that two normal populations have the same variance.Notionally, any F-test can be regarded as a comparison of two variances, but the specific case being discussed in this article is that of two populations, where the test statistic used is the ratio of two sample variances. [1]
The following numerical example illustrates Lindley's paradox. In a certain city 49,581 boys and 48,870 girls have been born over a certain time period. The observed proportion x {\displaystyle x} of male births is thus 49 581 / 98 451 ≈ 0.5036.
A two-tailed test is appropriate if the estimated value is greater or less than a certain range of values, for example, whether a test taker may score above or below a specific range of scores. This method is used for null hypothesis testing and if the estimated value exists in the critical areas, the alternative hypothesis is accepted over the ...