In this example, we are performing an upper tailed test (H 1: μ> 191), with a Z test statistic and selected α =0.05. Select the appropriate test statistic.īecause the sample size is large (n >30) the appropriate test statistic is The research hypothesis is that weights have increased, and therefore an upper tailed test is used. The investigator can then determine statistical significance using the following: If p 191 α =0.05 Statistical computing packages will produce the test statistic (usually reporting the test statistic as t) and a p-value. The hypotheses (step 1) should always be set up in advance of any analysis and the significance criterion should also be determined (e.g., α =0.05). In fact, when using a statistical computing package, the steps outlined about can be abbreviated. Statistical computing packages provide exact p-values as part of their standard output for hypothesis tests. The exact level of significance is called the p-value and it will be less than the chosen level of significance if we reject H 0. If the null hypothesis is rejected, then an exact significance level is computed to describe the likelihood of observing the sample data assuming that the null hypothesis is true. The final conclusion will be either to reject the null hypothesis (because the sample data are very unlikely if the null hypothesis is true) or not to reject the null hypothesis (because the sample data are not very unlikely). The final conclusion is made by comparing the test statistic (which is a summary of the information observed in the sample) to the decision rule.

Here we compute the test statistic by substituting the observed sample data into the test statistic identified in Step 2. The complete table of critical values of Z for upper, lower and two-tailed tests can be found in the table of Z values to the right in 'Other Resources.'Ĭritical values of t for upper, lower and two-tailed tests can be found in the table of t values in 'Other Resources.' Rejection Region for Lower-Tailed Z Test (H 1: μ 1.960. The decision rule is: Reject H 0 if Z > 1.645. Rejection Region for Upper-Tailed Z Test (H 1: μ > μ 0 ) with α=0.05 The decision rules are written below each figure. Notice that the rejection regions are in the upper, lower and both tails of the curves, respectively. The following figures illustrate the rejection regions defined by the decision rule for upper-, lower- and two-tailed Z tests with α=0.05.

For example, in an upper tailed Z test, if α =0.05 then the critical value is Z=1.645. The level of significance which is selected in Step 1 (e.g., α =0.05) dictates the critical value. The third factor is the level of significance.The appropriate critical value will be selected from the t distribution again depending on the specific alternative hypothesis and the level of significance. If the test statistic follows the t distribution, then the decision rule will be based on the t distribution. If the test statistic follows the standard normal distribution (Z), then the decision rule will be based on the standard normal distribution. The exact form of the test statistic is also important in determining the decision rule.In a two-tailed test the decision rule has investigators reject H 0 if the test statistic is extreme, either larger than an upper critical value or smaller than a lower critical value. In a lower-tailed test the decision rule has investigators reject H 0 if the test statistic is smaller than the critical value. In an upper-tailed test the decision rule has investigators reject H 0 if the test statistic is larger than the critical value. The decision rule depends on whether an upper-tailed, lower-tailed, or two-tailed test is proposed.The decision rule for a specific test depends on 3 factors: the research or alternative hypothesis, the test statistic and the level of significance. H 1: μ > μ 0, where μ 0 is the comparator or null value (e.g., μ 0 =191 in our example about weight in men in 2006) and an increase is hypothesized - this type of test is called an upper-tailed test.

For example, an investigator might hypothesize: An investigator might believe that the parameter has increased, decreased or changed. The research or alternative hypothesis can take one of three forms. Upper-tailed, Lower-tailed, Two-tailed Tests H 1: Research hypothesis (investigator's belief) α =0.05 H 0: Null hypothesis (no change, no difference) Set up hypotheses and select the level of significance α. The procedure can be broken down into the following five steps. We then determine whether the sample data supports the null or alternative hypotheses. Specifically, we set up competing hypotheses, select a random sample from the population of interest and compute summary statistics. The procedure for hypothesis testing is based on the ideas described above. Hypothesis Testing: Upper-, Lower, and Two Tailed Tests

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