I don't have enough rep to comment here, so I'm submitting a new answer to improve on dogbane's answer. The dot . in the regexp
[[ sed-4.2.2.tar.bz2 =~ tar.bz2$ ]] && echo matched
will actually match any character, not only the literal dot between 'tar.bz2', for example
[[ sed-4.2.2.tar4bz2 =~ tar.bz2$ ]] && echo matched
[[ sed-4.2.2.tar§bz2 =~ tar.bz2$ ]] && echo matched
or anything that doesn't require escaping with '\'. The strict syntax should then be
[[ sed-4.2.2.tar.bz2 =~ tar\.bz2$ ]] && echo matched
or you can go even stricter and also include the previous dot in the regex:
[[ sed-4.2.2.tar.bz2 =~ \.tar\.bz2$ ]] && echo matched