My 95 confidence interval is 2030 so there is a 95 chance th

Solution

whenever a confidence interval is computed it is based upon the given sample at hand.

now true mean is unknown to us. we are trying to estimate it on the basis of the given sample.

so to us true mean is a parameter not a random variable. but the confidence interval is random because it varies from sample to sample.

so if 95% confidence interval is (20,30) for the true mean then that does not mean that there is a 95% chance that the true mean is somewhere between 20 and 30. it means that there is a 95% chance that the random interval (20,30) will contain the true mean. here the interval is random. not the true mean. chance factor is associated with the random interval not with the true mean.