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If p is lower, you "reject the null hypothesis on a 5% (or 1%) level" in technical terms. You should have a cutoff value ready, such as 5% or 1%. When the value is sufficiently small, we reject the null hypothesis and conclude that the alternative hypothesis is true. p is the probability that the difference between the sample mean and μ 0 would occur if the null hypothesis is true.If the null hypothesis is true, it should be close to 0. z is the test statistic, the standardized difference between the sample mean and μ 0.The first line, involving μ, is the alternative hypothesis.In either case, it's important to understand the output of Z-Test. 0 indicates a two-sided hypothesis of μ≠ μ 0, -1 indicates μ μ 0.Īlthough you can access the Z-Test( command on the home screen, via the catalog, there's no need: the Z-Test… interactive solver, found in the statistics menu, is much more intuitive to use - you don't have to memorize the syntax. In either case, you can indicate what the alternate hypothesis is, by a value of 0, -1, or 1 for the alternative argument. However, in certain cases when we have reason to suspect the true mean is less than or greater than μ 0, we might use a "one-sided" alternative hypothesis, which will state that the true mean μ μ 0.Īs for the Z-Test( command itself, there are two ways of calling it: you may give it a list of all the sample data, or the necessary statistics about the list - its size, and the mean. In addition to the null hypothesis, we must have an alternative hypothesis as well - usually this is simply that the true mean is not μ 0. If, on the other hand, the probability is not too low, we conclude that the data may well have occurred under the null hypothesis, and therefore there's no reason to reject it. If this probability is sufficiently low (usually, 5% is the cutoff point), we conclude that since it's so unlikely that the data could have occurred under the null hypothesis, the null hypothesis must be false, and therefore the true mean μ is not equal to μ 0. To do this, we assume that this "null hypothesis" is true, and calculate the probability that the variation from this mean occurred, under this assumption. The logic behind a Z-Test is as follows: we want to test the hypothesis that the true mean of a population is a certain value ( μ 0). In addition, either the population must be normally distributed, or the sample size has to be sufficiently large. This test is valid for simple random samples from a population with a known standard deviation.
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Z-Test( performs a z significance test of a null hypothesis you supply. (outside the program editor, this will select the Z-Test… interactive solver) Z-Test( μ 0, σ, sample mean, sample size, //draw?//