How do I find the Critical Value?

How do I find the critical z value?

• Find the critical z value using a significance level of alpha = 0.1 if the alternative hypothesis Ho is mu > 35 How do I do this?

• Answer:

  Alpha value indicates the level of significance and the rejection region. In case of two tailed test the rejection region lies equally in both the tails whereas in case of one tailed test the rejection region lies in one tail concerned The sign in Ha indicates whether the test is one tailed or two tailed. if it is NOT = --- is a case of two tailed test if it is < --- it is a case of left tailed test if it is > --- it is a case of right tailed test Since alpha = 0.1 and Ha contained > sign, the rejection region 0.1000 area lies in extreme right tail of the normal curve. The z value which separates top 0.1000 area from the rest is the critical value of z When simple z-scores chart is consulted, it can be determined that z = 1.282 will separate the top 0.1000 area from the rest. Therefore, the critical value of z (zc) required in this case is + 1.282 zc is +ve because it is a case of right tailed test NOTE: zc values given below are to be remembered. When alpha = 0.1 for left tailed test - 1.282 for right tailed test + 1.282 for two tailed test +/- 1.645 When alpha = 0.05 for left tailed test - 1.645 for right tailed test + 1.645 for two tailed test +/- 1.96 When alpha = 0.01 for left tailed test - 2.327 for right tailed test + 2.327 for two tailed test 2.575