What should the outbound SMTP configuration be for Office 365 Exchange?
Which version of civi are you using? https://issues.civicrm.org/jira/browse/CRM-14814 it's fixed on a fairly recent version of civicrm only

Another reason can be the confirguration of your network or your server: can you start a connection on port 587 to smtp.office365.com ?

However, before you spend too much time on it, last time I checked:
- smtp on office365 was limited in volume, ie find at low volume, but won't work for production
- 365 doesn't handle "+" notation, so and email to bounce+something@yourdomain.org won't end up in your bounce mailbox. This is needed to handle bounces in civicrm

so I would recommend you:
if it's for testing purpose, use a gmail account
if it's for production purpose, use an external provider to do the bulk mailing and integrate it with your civi, for instance sendgrid and this extension:
https://civicrm.org/extensions/sendgrid-event-notification-processor