Critical Value
Where first derivative is 0 or undefined
A critical value is a value that is compared to a test statistic to determine whether or not the null hypothesis should be rejected. In hypothesis testing, the null hypothesis is the statement being tested, and the critical value is used to identify the rejection region.
The critical value depends on the significance level of the test and the degrees of freedom. The significance level is the probability of rejecting the null hypothesis when it is actually true, and it is usually set at 0.05 or 0.01. The degrees of freedom are a measure of the amount of variability present in the data, and they depend on the sample size and the number of parameters being estimated.
To find the critical value, you can use a standard table or a statistical software program. For example, if you are conducting a t-test with a sample size of 10 and a significance level of 0.05, and you have calculated a t-statistic of 2.5, you would consult a t-distribution table with 9 degrees of freedom (n-1). At a significance level of 0.05 and 9 degrees of freedom, the critical value would be 2.262.
If the calculated t-statistic is greater than the critical value, then the null hypothesis is rejected. If the calculated t-statistic is less than the critical value, then the null hypothesis cannot be rejected.
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