Help hiding root directory

I stared another thread with this question but for some reason it was closed. Here’s my problem:

I have a shared hosting account and have several websites hosted on that account. The very first domain I hosted is the main domain on the hosting account. As I add more domains, they are added as sub-folders.

For example: Lets say my main domain name is “examplesite.com”. Now I add a few more domains to the hosting account and one of them is “gypsyexample.com”. The “gypsyexample.com domain” is put on my hosting account and it is a sub-folder of “examplesite.com”

I want to install WordPress on the “gypsyexample” domain and when I do it through my web host, I have to go through the “examplesite.com” domain to do it because that is the parent domain on my hosting account. As I’m going through the process of installing WordPress, I have to choose to install it in a folder like this – “www.examplesite.com/gypsyexample”. So I did this. Now, when I open the blog – in the address bar of the browser, all of the pages are showing “www.examplesite.com/gypsyexample”. I don’t want the parent directory to show up. I just want the actual domain where I installed WordPress to show up.

How do I change things so when people go to various pages on the blog they don’t see the root directory before the domain the blog is hosted on?

Thanks so much for your help!