Do not thoroughly understand, but this is what I came up with:
To construct a confidence interval around a mean or around a difference between two means, the basic formula is: (sample statistic) ± (test statistic)(standard error of sample statistic). The value of the test statistic (either a z or a t) is the same for both the + and the – side. This is not the case when constructing a confidence interval around a sample variance.
Why?
The confidence interval is not symmetric about the sample variance. This contrasts with confidence intervals for the distribution mean, which are always symmetric about the sample mean.
To construct a confidence interval around a mean or around a difference between two means, the basic formula is: (sample statistic) ± (test statistic)(standard error of sample statistic). The value of the test statistic (either a z or a t) is the same for both the + and the – side. This is not the case when constructing a confidence interval around a sample variance.
Why?
The confidence interval is not symmetric about the sample variance. This contrasts with confidence intervals for the distribution mean, which are always symmetric about the sample mean.