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In general, the subscript 0 indicates a value taken from the null hypothesis, H 0, which should be used as much as possible in constructing its test statistic. ... Definitions of other symbols: Definitions of other symbols:
A possible null hypothesis is that the mean male score is the same as the mean female score: H 0: μ 1 = μ 2. where H 0 = the null hypothesis, μ 1 = the mean of population 1, and μ 2 = the mean of population 2. A stronger null hypothesis is that the two samples have equal variances and shapes of their respective distributions.
The consistent application by statisticians of Neyman and Pearson's convention of representing "the hypothesis to be tested" (or "the hypothesis to be nullified") with the expression H 0 has led to circumstances where many understand the term "the null hypothesis" as meaning "the nil hypothesis" – a statement that the results in question have ...
the exact sampling distribution of T under the null hypothesis is the binomial distribution with parameters 0.5 and 100. the value of T can be compared with its expected value under the null hypothesis of 50, and since the sample size is large, a normal distribution can be used as an approximation to the sampling distribution either for T or ...
The Shapiro–Wilk test tests the null hypothesis that a sample x 1, ..., x n came from a normally distributed population. The test statistic is = (= ()) = (¯), where with parentheses enclosing the subscript index i is the ith order statistic, i.e., the ith-smallest number in the sample (not to be confused with ).
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 ...
Since the null hypothesis for Tukey's test states that all means being compared are from the same population (i.e. μ 1 = μ 2 = μ 3 = ... = μ k), the means should be normally distributed (according to the central limit theorem) with the same model standard deviation σ, estimated by the merged standard error, , for all the samples; its ...
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.