How do I find the Critical Value?

How do you find the critical value in stats?

• What's the formula? Or what info do you have to put into your calculator?

• Answer:

  In hypothesis testing, the critical value is a number that separates a region where the null hypothisis will not be rejected from a region where it will be rejected. Take the usual easy problem about an average of a very large number of measurements so the sample mean is approximately normally distributed. Say that the standard error is 5. We make a null and alternate hypothesis, e.g. H0: mean=44 H1: mean not= 44 We will reject H0 (at the alpha=0.05 significance level) if the sample mean is below 44-1.96*5 or if it is above 44+5*1.96 Roughly 34 and 54 are the critical values for this test. If you instead, convert to a standard normal, you may call -1.96 and 1.96 the critical values. This usually is the case when asked to do a hypothesis test. If you have a TI-83, 2nd DISTR, 3:invnorm(0.025, 44,5)=34.2 invnorm(0.975,44,5) = 53.8 invnorm(0.025,0,1) = -1.96 invnorm(0.975,0,1)= 1.96 There is no inverse on TI-83 for the t-distribution so you need tables. For a one tail test, there is only one critical value. You really need to draw a picture of your test situation and know on which tail the reject region lies.