The phrase "doubted whether or not" is a grammatically correct phrase that is commonly used in written English.
It is typically used in sentences where the subject is unsure or uncertain about something. Example: The detective doubted whether or not the suspect was telling the truth about his alibi.
"People doubted whether or not I had the stamina," Mr. Thompson said to a packed room of supporters at a hotel here, adding that he has been "shaking hands like I've never shaken before".
You'll recall that fancy-pants analysts doubted whether or not Black Ops would reach the same kind of penetration that its predecessor, Modern Warfare 2, did.
There were some who doubted whether or not Gardena Serra could actually play with the likes of the many formidable opponents in the re-aligned, seven-team Mission League.
"You doubt whether or not they're trying to create a nuclear bomb?" Mr. Graham persisted.
Why is Mr. Woodward "doubting" whether or not Mr. Felt is "competent" to tell his story?
Until he does those things, people will doubt whether or not he really won Ohio.
He is easygoing and enjoys listening to Edward's stories of his homeworld, and while he doubts whether or not they are true and is hurt by how distant Edward behaves, he is nonetheless supportive of his efforts.
This is why one survivor once told me that after she reported her sexual assault to the police, she thought to herself, "I wish I was murdered instead so nobody had to doubt whether or not I was really raped".
Americans today are pretty sure that the government's postal service will deliver their mail on time, but they have every reason to doubt whether or not Chrysler, GM, AIG and Bear Stearns will be doing business tomorrow.
A number of employees also doubt whether or not parents, specifically mothers, are interested in internet-based support instead of "more personal contacts" [[ 58], p. 181].
This group of maybe-intenders might include people who never actually thought about using a self-test but who did not want to reject the possibility of ever using a self-test beforehand as well as of people who actually doubt whether or not to use a self-test.
