How do I find the Critical Value?

Statistics: How do I find the critical value and rejection regions?

• a random sample of 85 eighth grade students has a mean score of 265 with a standard deviation of 55 on a national mathematics assessment test. This test result prompts a state school administrator to declare that the mean score for the state’s eighth graders on the examination is more than 260. At α 0.04 , is there enough evidence to support the administrator's claim? Find the critical value and rejection regions? ( In the exercises that I have done before α usually equals .10, .05, .025, etc. so I just look at df (in this case 84 and the α column in the t distribution table but I don't know how to find a critical value with α=0.04

• Answer:

  Kristen - You have two choices ... use linear interpolation between α=0.025 and α=0.05, or use a statistical calculator like the TI-84 that has an InvT function. The critical value is 1.772 with d.f. = 84 and α=0.040. This assumes a "one-tail" test since the administrator states " is more than 260". Hope that helps.