How Effective Is Inverting a Test Statistic for New Confidence Intervals?

[ghostyc]

A very powerful method of construction of a confidence interval/set for an unknown parameter, the mean of a normal distribution for example, is to invert a family of hypotheses tests about that parameter. This project is firstly to demonstrate the understanding of this method by using it to construct the usual one-sided and two-sided confidence intervals for the unknown mean of a normal distribution with a known variance. But the prize is given if a new confidence interval can be constructed by using this method for the unknown mean of a normal distribution with a known variance.

Here, `A new confidence interval' means a confidence interval that is
different from the usual one-sided and two-sided confidence intervals
for the unknown mean of a normal distribution with a known variance.

Hi,

Can someone kindly explain a bit on the 'red' part.
I have tried to search for it, but nothing much related seem to come out.
You may not tell me what it is, all I need is some related resource ( section in a book, or a website, or an article? )

Thanks.

 

[ghostyc]

Hi there,

I finally see something here.

Is there any possibility that the 'red' part is referering to the pivotal interval?

Thanks.

I am a bit desperate now.

 

[ghostyc]

slowly giving up on this one