To find the critical value for a 94% confidence level, follow these steps:
1. Determine the alpha level:
- The confidence level is the probability that the true parameter lies within the confidence interval. For a 94% confidence level, the remaining probability (alpha) is [tex]\(1 - 0.94 = 0.06\)[/tex].
2. Divide the alpha level by 2 for a two-tailed test:
- In a two-tailed test, the total alpha level is split between the two tails of the normal distribution. Therefore, [tex]\(\alpha / 2 = 0.06 / 2 = 0.03\)[/tex].
3. Convert this value to a cumulative probability:
- Since 0.03 in each tail corresponds to the upper tail for one side of the normal distribution, the cumulative probability we are interested in is [tex]\(1 - 0.03 = 0.97\)[/tex].
4. Find the z-score for the cumulative probability:
- The critical value is the z-score that corresponds to a cumulative probability of 0.97 in the standard normal distribution.
5. Round the result to two decimal places:
- The critical value for a cumulative probability of 0.97 is 1.88 when rounded to two decimal places.
Therefore, the critical value for a 94% confidence level is [tex]\( \boxed{1.88} \)[/tex].
