Question

What is the α level if the confidence level is 10%?

0.10

0.90

10%

There is no relationship between the α level and the confidence level

Answer 1

If the confidence level is 10%, the α level is its complement, which would be 90% or 0.90.

Step-by-step explanation:

If the confidence level is 10%, this means that there is an overall probability of 10% that any given confidence interval contains the true population parameter. Therefore, the α level, also known as the significance level, is the complement of the confidence level. Since the confidence level is 10%, the α level is 1 - 0.10, which is 0.90 or 90%.

Mathematically, we can represent the relationship between the confidence level (CL) and the α level as CL = 1 - α. Hence, if CL = 10% or 0.10, then α = 1 - 0.10, which equals 0.90 or 90%.

To put it another way, if one wishes to be 10% confident that the parameter is within the interval, they are accepting a 90% risk (α level) that the parameter is not within that interval. The α level essentially represents the likelihood of making a Type I error, that is, rejecting a true null hypothesis.