To clarify for anyone who is finding this question:
The answer is yes, you need a privacy policy for your app if you are using AdMob. Refer to: AdMob Help (bottom of the page).
... Additionally, your app's privacy policy may need to be updated to reflect the use of personalized advertising (formerly known as interest-based advertising) served via the Google Mobile Ads SDK. Please take a moment to review your app's privacy policies and ensure that they are up-to-date. Because publisher pages and laws vary across countries, we're unable to suggest specific privacy policy language...
They essentially want you to inform users about the use of targeted advertising. They don't explicitly tell you what to write though.
Personally I think it should be enough to write something about that you use AdMob to serve ads and that AdMob uses the devices advertising id to serve personalized ads based on the users interests (which includes collecting and analyzing user data). A link to the Google page to opt-out of personalized advertising and to Googles Privacy Policies (here and here) can't hurt.
This also suggests that you need to have at least a link to your privacy policy in your app and on the store page. But maybe AdMob doesn't count as handling sensitive data, so maybe the link to the policy on the store page is optional in this case.
As a side note: If you use any Google Services (e.g. Location, Firebase, Places Api) you probably need a privacy policy