State whether or not the following is true. Explain why: Someone says that a computed result (0.06,0.07) of a 95% confidence interval of a parameter, β, implies that P[0.06 < β < 0.07] = 0.95.
It seems to me that the above statement is true. However, my instinct somehow tells me that it is not.
Any ideas?
Let me attempt to describe what is going on with confidence intervals. I'll probably muddle it at a few points.
In the frequentist model, $\beta$ is not a random variable and thus it does not make sense to talk about the probability of $\beta$ being within the two values given in a confidence interval. The probability statement in the frequentist model is about the construction of the intervals, the probability that the interval constructed in a certain manner will contain the actual parameter.
In the Bayesian model, $\beta$ is a random variable and you can talk about the probability of the parameter.
It is more nuanced than this, I recommend reading any good discussion on CIs to see what is really going on.