The number of outbound links will not lower your pagerank with google. Your pagerank is determined by how many inbound links are coming to your site and what the pagerank is of the sites that are pointing those links to you.
BUT!!
You need to be very careful when you are linking to other people. If you link to websites that google thinks of as spam it makes it more likely that google will also consider your own website to be spam. Only link to sites that are of high quality and are relevant and useful to your visitors.
Another issue is if you are making a link trade with someone so their site points to your and your site points to theirs google can also see this as a sign of spam. The value of reciprocal links has gone down a lot lately however they can still work sometimes.
In summary: No it won’t lower your pagerank but if you link to spammy or bad neighborhood websites this can hurt your rankings by google applying a spam penalty.