Question

which of the following is not true of the confidence level of a confidence interval?
choose the correct answer below.
a. the confidence level is often expressed as the probability or area ( 1 - alpha ), where ( alpha ) is the complement of the confidence level.
b. there is a ( 1 - alpha ) chance, where ( alpha ) is the complement of the confidence level, that the true value of ( p ) will fall in the confidence interval produced from our sample.
c. the confidence level is also called the degree of confidence.
d. the confidence level gives us the success rate of the procedure used to construct the confidence interval.

Explanation:

• Option A: The confidence level is indeed often expressed as \(1 - \alpha\), where \(\alpha\) is the complement. For example, a 95% confidence level has \(\alpha=0.05\).
• Option B: The confidence level represents the success rate of the procedure. It is not about the probability that the True value of \(p\) (a parameter) will fall in the interval. The parameter \(p\) is a fixed value (either it is in the interval or not). The confidence level is about the long - run success rate of the method.
• Option C: "Confidence level" and "degree of confidence" are synonymous terms.
• Option D: The confidence level does give the success rate of the procedure. If we construct many confidence intervals using the same method, the proportion of intervals that contain the True parameter value is equal to the confidence level.

Answer:

B. There is a \(1-\alpha\) chance, where \(\alpha\) is the complement of the confidence level, that the true value of \(p\) will fall in the confidence interval produced from our sample.