The sample proportion is never equal to the population proportion

We expect 95% confidence intervals to contain the sample proportion 95% of the time

Are the above statements true? I would say yes because the sample proportion is not the same as the population proportion and the if you have a 95% confidence interval than the sample proportion should contain it 95% of the time. Are these statements true?

Yes, both statements are true.

The sample proportion refers to the proportion observed in a sample, while the population proportion refers to the proportion in the entire population being studied. In most cases, the sample proportion is not expected to be exactly equal to the population proportion due to random sampling variation.

Regarding the second statement, a 95% confidence interval is an interval estimate that is constructed in a way that it has a 95% chance of containing the true population parameter (in this case, the population proportion). This means that if we repeatedly sample and construct 95% confidence intervals, about 95% of those intervals would successfully contain the true population proportion. So, it is expected that the sample proportion will fall within the 95% confidence interval approximately 95% of the time.