I hadn't particular problems with the first two parts, but I started to struggle while doing this third part. If I understood, I've to compute a confidence interval by using the likelihood ratios. So I've to find the values that satisfy the inequality:

So they subtracted, from the likelihood function with respect to a generic parameter p, the likelihood of the sampling estimator ( ), obviously putting this subtraction greater or equal to

**-1.92**

The aim is to find a value of p such that its likelihood is equal or greater than the log-lik on the estimator minus

**1.92**. But so, how can I obtain, from this computation, a limited interval like the one in the photo (

**p**belonging to

**[0.183,0.51]**. In particular, I don't understand how it is possible to arrive, from the inequality to that interval. How is it possible to estimate the parameter for which the difference between the log-lik of

**p**and the log-lik of is the biggest one?

I'm sorry if my question could appear a bit confused, it may be connected to the fact that I haven't such a big knowledge about chi-squared distribution (I only know that a chi-squared random variable refers to the sum of some squared standard normal variables). So I don't know, in general, how to use the chi-squared distribution to build confidence intervals.