The computed test statistic is also known as the critical value.
true or false
False.
The computed test statistic and the critical value are not the same; they are related concepts used in hypothesis testing but serve different purposes:
1. Computed Test Statistic: It is the value calculated from your sample data using a specific statistical test (e.g., t-test, z-test, chi-square test). It reflects the degree to which the sample data deviates from the null hypothesis. The test statistic takes into account both the sample size and the difference between the observed data and the values expected under the null hypothesis.
2. Critical Value: This is a cutoff point derived from the probability distribution of the test statistic under the null hypothesis. The critical value determines the threshold at which you will reject the null hypothesis. It depends on the significance level (alpha) chosen for the test and the distribution of the test statistic. If the absolute value of the computed test statistic is greater than the critical value, the null hypothesis is rejected.
For example, in a two-tailed z-test with a significance level of 0.05, the critical value is generally 1.96. If the computed z-test statistic is greater than 1.96 or less than -1.96, you would reject the null hypothesis. The choice of critical value is based on the desired confidence level and the type of test being performed (one-tailed or two-tailed).
Therefore, we use the computed test statistic to compare against the critical value to decide whether our results are statistically significant.