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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 ...
In addition, we suppose that the measurements X 1, X 2, X 3 are modeled as normal distribution N(μ,2). Then, T should follow N(μ,2/) and the parameter μ represents the true speed of passing vehicle. In this experiment, the null hypothesis H 0 and the alternative hypothesis H 1 should be H 0: μ=120 against H 1: μ>120.
The hypothesis would have fit the observation much better than almost all other ratios, including For example, this choice of hypotheses and prior probabilities implies the statement "if θ {\displaystyle \theta } > 0.49 and θ {\displaystyle \theta } < 0.51, then the prior probability of θ {\displaystyle \theta } being exactly 0.5 is 0.50/0. ...
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 ...
where X k is the number of times outcome k is observed. If the null hypothesis of "fairness" is true, then the probability distribution of the test statistic can be made as close as desired to the chi-squared distribution with 5 degrees of freedom by making the sample size n sufficiently large.
In 1970, L. A. Marascuilo and J. R. Levin proposed a "fourth kind of error" – a "type IV error" – which they defined in a Mosteller-like manner as being the mistake of "the incorrect interpretation of a correctly rejected hypothesis"; which, they suggested, was the equivalent of "a physician's correct diagnosis of an ailment followed by the ...
An example of the first resample might look like this X 1 * = x 2, x 1, x 10, x 10, x 3, x 4, x 6, x 7, x 1, x 9. There are some duplicates since a bootstrap resample comes from sampling with replacement from the data. Also the number of data points in a bootstrap resample is equal to the number of data points in our original observations.