For a two-tailed hypothesis test using a 5% significance level, what is the critical value of $z$?

• A. $\pm 1.96$
• B. $\pm 2.33$
• C. $\pm 1.645$
• D. $\pm 2.58$

Answer: (A)

Verified step by step guidance

1. Understand that a two-tailed hypothesis test at a 5% significance level means the total area in both tails of the standard normal distribution is 0.05.
2. Since the test is two-tailed, split the significance level equally between the two tails, so each tail has an area of 0.025.
3. To find the critical value \( z \), look up the z-score that corresponds to the cumulative probability of \( 1 - 0.025 = 0.975 \) in the standard normal distribution table.
4. The critical values will be symmetric around zero, so the critical values are \( \pm z_{0.975} \), where \( z_{0.975} \) is the z-score found in the previous step.
5. These critical values define the rejection regions for the hypothesis test: if the test statistic falls outside \( \pm z_{0.975} \), reject the null hypothesis.