Compute the critical value zα/2.
Understand the Problem
The question is asking for the critical value of the standard normal distribution for a given significance level a/2, which is typically used in statistical hypothesis testing or confidence interval calculations.
Answer
The critical value is $z = 1.96$.
Answer for screen readers
The critical value of the standard normal distribution for a significance level of $\alpha/2 = 0.025$ is approximately $z = 1.96$.
Steps to Solve
- Identify the significance level
The significance level is denoted by $\alpha$. For a two-tailed test, you will need to divide this by 2, so ( \alpha/2 ) is used.
- Find the corresponding critical value
We need to find the critical value $z_{\alpha/2}$ that corresponds to $1 - \frac{\alpha}{2}$ in standard normal distribution tables, or you can use statistical software or a calculator.
- Using the Z-table or software
Look up the value in the Z-table or calculate it. If you have a significance level $\alpha = 0.05$, then $\alpha/2 = 0.025$. We look for the Z value for $1 - 0.025 = 0.975$.
- Determine the critical value
The critical value $z_{0.025}$ for $\alpha = 0.05$ is typically found to be approximately $1.96$. Therefore, the critical values are $-1.96$ and $1.96$.
The critical value of the standard normal distribution for a significance level of $\alpha/2 = 0.025$ is approximately $z = 1.96$.
More Information
The critical value of $1.96$ is significant because it is commonly used in statistical tests, such as when calculating confidence intervals. It implies that for a 95% confidence level, the area under the normal curve within this range will include approximately 95% of the population.
Tips
- Forgetting to divide the significance level by 2 for two-tailed tests. Always make sure to use $\alpha/2$.
- Not checking the Z-table accurately or using the wrong side of the table. Make sure to look for the area corresponding to $1 - \frac{\alpha}{2}$.
AI-generated content may contain errors. Please verify critical information
