The online NPM documentation does not explain how to upgrade ember-cli-babel. I tried following the accepted answer posted here Invalid Version: Ember-Cli-Babel, but that did not work.
DEPRECATION: ember-cli-babel 5.x has been deprecated. Please upgrade to at least ember-cli-babel 6.6. Version 5.2.8 located: library-ui -> ember-clean-tmp -> ember-cli-babel
Update
I have uninstalled the Ember-clean-tmp add-on. When I run Ember-cli-update I get a message that says Tags match, nothing to apply. I then ran Ember S and get the following warnings:
WARNING: ember-basic-dropdown attempted to include external babel helpers to make your build size smaller, but your root app's ember-cli-babel version is not high enough. Please update ember-cli-babel to v7.3.0-beta.1 or later.
WARNING: ember-power-select attempted to include external babel helpers to make your build size smaller, but your root app's ember-cli-babel version is not high enough. Please update ember-cli-babel to v7.3.0-beta.1 or later.
WARNING: ember-data attempted to include external babel helpers to make your build size smaller, but your root app's ember-cli-babel version is not high enough. Please update ember-cli-babel to v7.3.0-beta.1 or later.
WARNING: ember-basic-dropdown attempted to include external babel helpers to make your build size smaller, but your root app's ember-cli-babel version is not high enough. Please update ember-cli-babel to v7.3.0-beta.1 or later.
WARNING: ember-text-measurer attempted to include external babel helpers to make your build size smaller, but your root app's ember-cli-babel version is not high enough. Please update ember-cli-babel to v7.3.0-beta.1 or later.
WARNING: ember-power-select attempted to include external babel helpers to make your build size smaller, but your root app's ember-cli-babel version is not high enough. Please update ember-cli-babel to v7.3.0-beta.1 or later.
Update 2
I was able to fix the issue by uninstalling ember-cli-babel and re-installing it, which got me to version 7.5.0. But, is this the correct way to upgrade packages?
The problem that you are experiencing is related to one of your addon's depending on an older version of ember-cli-babel.
From the deprecation notice, it's ember-clean-tmp, which doesn't look to be up to date. You have a number of options here. First, you could stop using the addon (which in this case doesn't really seem like a necessary addon. Needing to clear my tmp has never been a problem for me in my 2.18 app).
Secondly, if you'd like to keep using the addon, you could go through the process of upgrading the addon's ember-cli version to a version that includes a high enough ember-cli-babel version. Basically, each ember-cli version has a default blueprint for what dependencies a new app should include. When you ugprade, you diff your dependencies and various files against the default for that ember-cli version. ember-cli-update is an addon that makes this process nice. You can then point at your own fork or better yet, get your update merged upstream in ember-clean-tmp