What are the two critical values for a two-tailed test with a 0.01 level of significance when n is large and the population standard deviation is known?
A) Above 1.96 and below -1.96
B) Above 1.65 and below -1.65
C) Above 2.58 and below -2.58
D) Above 1.00 and below -1.00

Question

Quizplus · Accepted Answer

When n is large and population standard deviation is known, we use the z-distribution. For a 0.01 level of significance, we divide the significance level by two (because it's a two-tailed test), giving us 0.005 in each tail. Looking up the critical value in a standard normal distribution table, we find that the critical value is 2.58. The negative critical value is -2.58. Therefore, the two critical values are above 2.58 and below -2.58. Option C is the only one that includes the correct values.

What Are the Two Critical Values for a Two-Tailed Test