We will focus primarily on large samples. In such cases, we can use the results of the table given above to formulate decision rules. A twotailed test is more conservative than a onetailed test because a twotailed test takes a more extreme test statistic to reject the null hypothesis. The most common format is a two-tailed test, meaning the critical. In practice, you should use a onetailed test only when you have good reason to expect that the difference will be in a particular direction. Similarly, in the left-tailed (H1: μ 30), the sampling distributions of many statistics are approximately normal distribution. When testing a hypothesis, you must determine if it is a one-tailed or a two-tailed test. Μ > μ 0, the critical region (or rejection region) z > z α lies entirely in the right tail of the sampling distribution of sample statistic with area equal to the level of significance a. Probabilities in z-tables are accurate only for populations that follow a normal distribution. The main difference between one-tailed and two-tailed tests is that one-tailed tests will only have one critical region whereas two-tailed tests will have. The shaded area and its probability correspond to the z-score. It is easier to reject the null hypothesis with a one-tailed than with a two-tailed test as long as. In this case, the test is a single-tailed or one-tailed test. This z-table chart is a probability distribution plot displaying the standard normal distribution. The figure shows that the one-tailed probability is 0.036. If the test is one-tailed either right-tailed or left-tailed), then the test is called a one-tailed test.įor example, to test whether the population mean μ = μ 0, we may have the Alternative Hypothesis H1 given by H1: μ μ 0 (Right-tailed). If the test is two-tailed, H1: μ ≠ μ 0 then the test is called two-tailed test and in such a case the critical region lies in both the right and left tails of the sampling distribution of the test statistic, with total area equal to the level of significance as shown in diagram.
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