6:357:50How To Find Rejection Regions And Critical Values Using AZ TestYouTubeStart of suggested clipEnd of suggested clipOn our graph you can see that the standardized test statistic does fall in the rejection region toMoreOn our graph you can see that the standardized test statistic does fall in the rejection region to the right as Z the standardized test statistic is greater than positive Z naught the critical.
In a two-sided test the null hypothesis is rejected if the test statistic is either too small or too large. Thus the rejection region for such a test consists of two parts: one on the left and one on the right. For a left-tailed test, the null hypothesis is rejected if the test statistic is too small.
Rejecting or failing to reject the null hypothesis If our statistical analysis shows that the significance level is below the cut-off value we have set (e.g., either 0.05 or 0.01), we reject the null hypothesis and accept the alternative hypothesis.
A critical region, also known as the rejection region, is a set of values for the test statistic for which the null hypothesis is rejected. i.e. if the observed test statistic is in the critical region then we reject the null hypothesis and accept the alternative hypothesis.
Generally, the test statistic is calculated as the pattern in your data (i.e. the correlation between variables or difference between groups) divided by the variance in the data (i.e. the standard deviation).
A test statistic is the value used in a hypothesis test to decide whether to support or reject a null hypothesis. This statistic compares data from an experiment or sample to the results expected from the null hypothesis.
To graph a significance level of 0.05, we need to shade the 5% of the distribution that is furthest away from the null hypothesis. In the graph above, the two shaded areas are equidistant from the null hypothesis value and each area has a probability of 0.025, for a total of 0.05.
A p-value less than 0.05 (typically ≤ 0.05) is statistically significant. It indicates strong evidence against the null hypothesis, as there is less than a 5% probability the null is correct (and the results are random). Therefore, we reject the null hypothesis, and accept the alternative hypothesis.
The decision rule at a significance level of 0.05 is reject the null hypothesis if the test statistic is less than -1.96 or greater than 1.96. (These will always be the critical values for a two-tailed test with significance of 5%).
The rejection region is the region where, if our test statistic falls, then we have enough evidence to reject the null hypothesis. If we consider the right-tailed test, for example, the rejection region is any value greater than c 1 − α , where c 1 − α is the critical value.
Here we use significance level α = 0.05, therefore the rejection region is when z > 1.645. 4.
How to calculate p-value from test statistic?Left-tailed test: p-value = cdf(x)Right-tailed test: p-value = 1 - cdf(x)Two-tailed test: p-value = 2 * min{cdf(x) , 1 - cdf(x)}