We cannot interpret the confidence interval estimate of μ as a probability statement about μ because the population mean is a fixed quantity.

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A confidence interval estimate provides a range of values within which we expect the true population parameter (in this case, the population mean) to lie with a certain level of confidence. It is not a statement of probability about the population parameter itself, as the parameter is a fixed quantity and not a random variable. Confidence intervals are based on random samples drawn from the population, and their purpose is to provide information about the precision of our estimate, not the probability of different values for the population parameter.

We Cannot Interpret the Confidence Interval Estimate of μ as a Probability