[I removed pgsql-hackers@lists.postgresql.org address from this reply since it looked like agreement this does not belong there. However one said this belongs on the pgadmin-support@lists.postgresql.org list, and another said it belongs on pgsql-admin@lists. postgresql.org, so I kept both here; I hope okay.]

Hello, 

I appreciate all the response. Here are my replies, in purple below:
1. What is your operating system? It looks like Windows, but I'm not sure. Also what version number for the OS?

Windows 10 
Version 1803 (OS Build 17134.407)

2. Look in the url. You are at 127.0.0.1. That is the same as localhost. But then it says 49194. 

I don't see 49194.

Postgres uses 5432 by default. That's why you got that part of the error message, but we need a lot more detail to help you. 

3. It might be that your OS is too old to run the more recent versions of Postgres. I don't use Windows anymore, but I know you have to be at Ubuntu 18 to run PG 10 +, there's probably something similar in Windows. That is one of the many reasons why knowing your OS is important information.
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Another reply

How come.  (Are you running a really old distro version?)

No.

Well, is Postgres running?  You installed Pg but did you start it?  

I can launch pgAdmin, but I cannot log into postgres. Instead I receive the error message cited below.

These two commands will tell you:
pg_ctl status # when logged in as user postgres
sudo netstat -an | grep 5432


On Fri, Nov 23, 2018 at 8:31 PM Anne Marie Harm <amharm@earthlink.net> wrote:
Hello, 

Unfortunately I'm unable to operate pgAdmin/PostgreSQL; first of all I can only install version 9.5 (tried versions 11, 10, and 9.6 -- but cannot install). When I launch pgAdmin in order to try to use PostgreSGL 9.5, h
ere is the full text of the error message I receive (also, screenshot attached):

could not connect to server: Connection refused (0x0000274D/10061) Is the server running on host "localhost" (::1) and accepting TCP/IP connections on port 5432? could not connect to server: Connection refused (0x0000274D/10061) Is the server running on host "localhost" (127.0.0.1) and accepting TCP/IP connections on port 5432?

Please advise; thank you. ~ Anne Marie
----------------------------
Anne Marie Harm
(312) 563-9397
amharm@earthlink.net
https://www.linkedin.com/in/annemarieharm