Find $\alpha$ for a 90% confidence interval.

• A. $\alpha=0.90$
• B. $\alpha=0.10$
• C. $\alpha=0.05$
• D. $\alpha=0.01$

Answer: (B)

Verified step by step guidance

1. Understand that the confidence level of a confidence interval is the probability that the interval contains the true parameter value. For a 90% confidence interval, this means we are 90% confident that the interval contains the true parameter.
2. The confidence level is denoted by (1 - α), where α is the significance level. Therefore, for a 90% confidence interval, we have 1 - α = 0.90.
3. To find α, rearrange the equation: α = 1 - confidence level. Substitute the confidence level with 0.90.
4. Calculate α by subtracting the confidence level from 1: α = 1 - 0.90.
5. Interpret the result: α represents the probability of the interval not containing the true parameter value, which is the complement of the confidence level.