The adjusted 95% interval for the proportion based on a small sample is shorter than the usual 95% -interval. Does that mean that the coverage of the adjusted interval is less than 95%? Explain. An...

The adjusted 95% interval for the proportion based on a small sample is shorter than the usual 95%
-interval. Does that mean that the coverage of the adjusted interval is less than 95%? Explain.

An analyst decided to use either the 95% t-interval for the mean or the corresponding 95% interval for the median, whichever was shorter. His sample was symmetric, so the mean and median are roughly the same in his population. What do you think of this approach?