Question
Find the critical value Zva/2 needed to construct a confidence interval with level 96%.
Round the answer to two decimal places.
Round the answer to two decimal places.
Answers
GPT-4o mini
To find the critical value \( Z_{\alpha/2} \) for a confidence level of 96%, you first need to determine \( \alpha \), which is the complement of the confidence level.
The confidence level is 96%, so:
\[
\alpha = 1 - 0.96 = 0.04
\]
Since this is a two-tailed test, you divide \( \alpha \) by 2:
\[
\alpha/2 = \frac{0.04}{2} = 0.02
\]
Now, you need to find the z-score that corresponds to \( 1 - \alpha/2 = 1 - 0.02 = 0.98 \).
Using a standard normal distribution table or a calculator, you can find that:
\[
Z_{0.98} \approx 2.05
\]
Thus, the critical value \( Z_{\alpha/2} \) needed to construct a confidence interval with a level of 96% is approximately:
\[
\boxed{2.05}
\]
The confidence level is 96%, so:
\[
\alpha = 1 - 0.96 = 0.04
\]
Since this is a two-tailed test, you divide \( \alpha \) by 2:
\[
\alpha/2 = \frac{0.04}{2} = 0.02
\]
Now, you need to find the z-score that corresponds to \( 1 - \alpha/2 = 1 - 0.02 = 0.98 \).
Using a standard normal distribution table or a calculator, you can find that:
\[
Z_{0.98} \approx 2.05
\]
Thus, the critical value \( Z_{\alpha/2} \) needed to construct a confidence interval with a level of 96% is approximately:
\[
\boxed{2.05}
\]