Critical Values for Two-Tailed Hypothesis Test

B

For a level of significance of 0.01, we can find the z value by 1.0 - 0.505 = 0.495 which is 2.58.

The critical values for a two-tailed hypothesis test with an alpha level of 0.01 are determined based on the desired level of significance and the assumption of a normal distribution.

In a two-tailed test, the null hypothesis states that there is no significant difference or relationship between the variables being tested. The alternative hypothesis, on the other hand, suggests that there is a significant difference or relationship.

To determine the critical values, we need to divide the alpha level (0.01) equally between the two tails of the distribution. Since it's a two-tailed test, we have to consider both the left and right tails of the distribution.

To find the critical value for the left tail, we need to find the z-score that corresponds to an area of 0.005 in the left tail. In other words, we need to find the z-score such that the area to the left of that z-score is 0.005. Looking up this value in a standard normal distribution table or using statistical software, we find that the z-score is approximately -2.58 (option B).

Similarly, to find the critical value for the right tail, we need to find the z-score that corresponds to an area of 0.005 in the right tail. This is the same as the left tail but in the opposite direction. Since the normal distribution is symmetric, the z-score for the right tail is the negative of the z-score for the left tail, which is approximately +2.58.

Therefore, the critical values for a two-tailed hypothesis test with an alpha level of 0.01 are +/- 2.58 (option B).