go to admin > pages > hover over activity > click edit > untick guests

thank you, it is not working.
type www.mysite.com/index and you can see index page.

whats your website url?

also we can't to hide users/latest and online.

what settings are guest set to on

admin > permissions > roles

and

admin > permissions

there is no option to hide index or users from roles permissions.
show your site with hidden index for guests . no option

now I hide it from members too :( and guests also can see the index :D
it hides only navigation menu.
if I check visible for members and guests it is become gray , if I unchek both - also gray.
I tried to hide - not working.
in roles permissions there are no permissions for index page.

come to the conclusion - we can't to hide index page.

you could purchase the SEO plugin and change the index page to a very random link that no one will be able to guess 

why I could purchase this plugin, I want it (hide index) will be incuded in users permissions.
to hide index from users I can by changing the code. it is no problem for me.