The above formula allows you to assess whether or not there is a statistically significant difference between two means. How to calculate the test statistic for the two samples? We have that the formula for a z-statistic for two population means is: Type I error occurs when we reject a true null hypothesis, and the Type II error occurs when we fail to reject a false null hypothesis In a hypothesis tests there are two types of errors. The p-value is the probability of obtaining sample results as extreme or more extreme than the sample results obtained, under the assumption that the null hypothesis is true The main principle of hypothesis testing is that the null hypothesis is rejected if the test statistic obtained is sufficiently unlikely under the assumption that the null hypothesis The main properties of a one sample z-test for two population means are:ĭepending on our knowledge about the "no effect" situation, the z-test can be two-tailed, left-tailed or right-tailed The null hypothesis is a statement about the population means, corresponding to the assumption of no effect, and the alternative hypothesis is the complementary hypothesis to the null hypothesis. The test has two non-overlapping hypotheses, the null and the alternative hypothesis. ![]() More specifically, we are interested in assessing whether or not it is reasonable to claim that the two population means the population means \(\mu\)Īre equal, based on the information provided by the samples. Being able to calculate it will allow you to proceed on sure footing.So you can better use the results delivered by this solver: A z-test for two means is a hypothesis test that attempts to make a claim about the population means (\(\mu_1\) and \(\mu_2\)).
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