To find the value of [tex]\(\alpha\)[/tex] when given a confidence level of 74%, we can use the following steps:
1. Understand that the confidence level represents the proportion of times that the confidence interval would contain the true population parameter if the same population were sampled multiple times. In this case, the confidence level is 74%.
2. The value of [tex]\(\alpha\)[/tex] is the proportion of the distribution that falls outside the confidence interval. It is calculated as 1 minus the confidence level.
3. For a confidence level of 74%, we have:
[tex]\[
\alpha = 1 - \text{confidence level}
\][/tex]
4. Substituting the given confidence level (74% or 0.74), we get:
[tex]\[
\alpha = 1 - 0.74 = 0.26
\][/tex]
Therefore, the value of [tex]\(\alpha\)[/tex] is 0.26.
