Error establishing a database connection

I am installing WordPress for the first time. My hosting company provides Fantastico for the WordPress installation which they say has already run the installer for WordPress. I’m following a WordPress book that says even after uploading WP files and changing the wp-config.php file (which my hosting company confirmed is correctly set up), I need to go to my browser and run the WP installer which is inside the WP folder at wp-admin/install.php.

But I’m receiving this error:

Error establishing a database connection
This either means that the username and password information in your wp-config.php file is incorrect or we can’t contact the database server at localhost. This could mean your host’s database server is down.

Are you sure you have the correct username and password?
Are you sure that you have typed the correct hostname?
Are you sure that the database server is running?
If you’re unsure what these terms mean you should probably contact your host.
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So what else should I check so that the installer works. I’m using Mac OS 10.5.6 and I’ve tried using both Safari and Firefox browsers. Any assistance would be greatly appreciated. Thank you.