Please note that this solution requires that your android device be rooted. And I have confirmed this solution only on android 4.X.X upwards.
How to Correct PlayStore And Other Google Apps Connection Error
1- If your android device is not rooted, root it first.
2- Download and install any root file browser like Root Browser, ES File Explorer amongst others from the PlayStore.
3- Open the root explorer application and grant it root access.
4- Now, go to the phone's memory, locate etc folder. Inside the etc, locate hosts file and delete it.
5- Restart the phone and enjoy!